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Rohde, Christian

Christian Rohde

Prof. Dr.

Head of Group
Institute of Applied Analysis and Numerical Simulation
Chair of Applied Mathematics

Contact

+49 711 685 65524
+4971168565599
Email

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.131

Office Hours

Fridays 1:30 - 2:30 pm and by appointment

Publications

2022
1. Burbulla, S., & Rohde, C. (2022). A finite-volume moving-mesh method for two-phase flow in fracturing porous media. J. Comput. Phys., 111031. https://doi.org/10.1016/j.jcp.2022.111031
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  @article{burbulla2022finitevolume, abstract = {Multiphase flow in fractured porous media can be described by discrete fracture matrix models that represent the fractures as dimensionally reduced manifolds embedded in the bulk porous medium. Generalizing earlier work on this approach we focus on immiscible two-phase flow in time-dependent fracture geometries, i.e., the fracture itself and the aperture of the fractures might evolve in time. For dynamic fracture geometries of that kind, neglecting capillary forces, we deduce by transversal averaging of a full dimensional description a dimensionally reduced model that governs the geometric evolution and the flow dynamics. The core computational contribution is a mixed-dimensional finite-volume discretization based on a conforming moving-mesh ansatz. This finite-volume moving-mesh (FVMM) algorithm is tracking the fractures' motions as a family of unions of facets of the mesh. Notably, the method permits arbitrary movement of facets of the triangulation while keeping the mass conservation constraint. In a series of numerical examples we investigate the modeling error of the reduced model as it compares to the original full dimensional model. Moreover, we show the performance of the finite-volume moving-mesh algorithm for the complex wave pattern that is induced by the interaction of saturation fronts and evolving fractures.}, author = {Burbulla, Samuel and Rohde, Christian}, doi = {https://doi.org/10.1016/j.jcp.2022.111031}, journal = {J. Comput. Phys.}, pages = 111031, title = {A finite-volume moving-mesh method for two-phase flow in fracturing porous media}, url = {https://www.sciencedirect.com/science/article/pii/S0021999122000936}, year = 2022 }
  Link
  https://www.sciencedirect.com/science/article/pii/S0021999122000936
2. Magiera, J., & Rohde, C. (2022). A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces. J. Comput. Phys., 111551. https://doi.org/10.1016/j.jcp.2022.111551
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  @article{magiera.rohde:molecular:2022, abstract = {The dynamics of compressible liquid–vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid–vapor flow accurately, without imposing ad-hoc closure relations on the continuum scale. The multiscale model combines the Euler equations on the continuum scale with molecular-scale particle simulations that govern the interface motion. We rely on an interface-preserving moving mesh finite volume method to discretize the continuum-scale sharp-interface flow in a conservative manner. Computational efficiency, while preserving physical properties, is achieved by a surrogate solver for the interface dynamics based on constraint-aware neural networks. The multiscale model is presented in its general form, and applied to regimes of temperature-dependent liquid–vapor flow which have not been accessible before.}, author = {Magiera, J. and Rohde, C.}, doi = {https://doi.org/10.1016/j.jcp.2022.111551}, issn = {0021-9991}, journal = {J. Comput. Phys.}, pages = 111551, title = {A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces}, url = {https://www.sciencedirect.com/science/article/pii/S0021999122006131}, year = 2022 }
  Link
  https://www.sciencedirect.com/science/article/pii/S0021999122006131
3. Massa, F., Ostrowski, L., Bassi, F., & Rohde, C. (2022). An artificial Equation of State based Riemann solver for a discontinuous Galerkin discretization of the incompressible Navier–Stokes equations. J. Comput. Phys., 110705. https://doi.org/10.1016/j.jcp.2021.110705
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  @article{MassaOstrowskiBassiRohde21, abstract = {In this work we present a novel exact Riemann solver for an artificial Equation of State (EoS) based modification of the incompressible Euler equations. Differently from the well known artificial compressibility method, this new approach overcomes the lack of the pressure-velocity coupling by using a suitably designed artificial EoS. The modified set of equations fits into the framework of first order hyperbolic conservation laws. Accordingly, an exact Riemann solver is derived. This new solver has the advantage to avoid a wave pattern violation issue which can affect the exact Riemann problem solution obtained by the standard artificial compressibility approach. The new artificial EoS based Riemann solver can be used as a tool for the definition of the advective Godunov fluxes in a Finite Volume or a discontinuous Galerkin discretization of the incompressible Navier–Stokes (INS) equations. We assess and analyse the new exact Riemann solver on 1D Riemann problems. Its capability and effectiveness are then shown in the context of a high-order accurate discontinuous Galerkin discretization of the INS equations. In particular, we verify the convergence properties, both in space and time, considering two test cases in 2D, namely, the Kovasznay test case and a damped travelling waves test case. Finally, we perform an implicit large eddy simulation of the incompressible turbulent flow over periodic hills where the classic forcing term formulation is modified to deal with variable time steps. Solution comparisons with respect to numerical and experimental results from the literature are given.}, author = {Massa, F. and Ostrowski, L. and Bassi, F. and Rohde, C.}, doi = {https://doi.org/10.1016/j.jcp.2021.110705}, issn = {0021-9991}, journal = {J. Comput. Phys.}, pages = 110705, title = {An artificial Equation of State based Riemann solver for a discontinuous Galerkin discretization of the incompressible Navier–Stokes equations}, url = {https://www.sciencedirect.com/science/article/pii/S0021999121006008}, year = 2022 }
  Link
  https://www.sciencedirect.com/science/article/pii/S0021999121006008
4. Keim, J., Munz, C.-D., & Rohde, C. (2022). A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in onfined Domains. In arXiv e-prints. https://doi.org/0.48550/ARXIV.2208.05310
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  @preprint{Keim.Munz.rohde:NSK:2022, archiveprefix = {arXiv}, author = {Keim, Jens and Munz, Claus-Dieter and Rohde, Christian}, doi = {0.48550/ARXIV.2208.05310}, eprint = {2208.05310v1}, eprintclass = {physics.flu-dyn}, eprinttype = {arXiv}, journal = {arXiv e-prints}, langid = {english}, primaryclass = {physics.flu-dyn}, title = {A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in onfined Domains}, url = {https://arxiv.org/abs/2208.05310}, year = 2022 }
  Link
  https://arxiv.org/abs/2208.05310
5. Gander, M., Lunowa, S., & Rohde, C. (2022). Non-overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations. SIAM J. Sci. Comput. http://www.uhasselt.be/Documents/CMAT/Preprints/2021/UP2103.pdf
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  @article{gander2021nonoverlapping, author = {Gander, Martin and Lunowa, Stephan and Rohde, Christian}, journal = {SIAM J. Sci. Comput.}, title = {Non-overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations}, url = {http://www.uhasselt.be/Documents/CMAT/Preprints/2021/UP2103.pdf}, year = 2022 }
  Link
  http://www.uhasselt.be/Documents/CMAT/Preprints/2021/UP2103.pdf
6. Seus, D., Radu, F. A., & Rohde, C. (2022). Towards hybrid two-phase modelling using linear domain decomposition. Numerical Methods for Partial Differential Equations, n/a(n/a), Article n/a. https://doi.org/10.1002/num.22906
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  @article{seus2022towards, abstract = {The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g., in soil layers in contact with the atmosphere) the system can be substituted by the scalar Richards model. Thus, the porous medium domain may be partitioned into disjoint subdomains where either the full two-phase or the simplified Richards model dynamics are valid. Extending the previously considered one-model situations we suggest coupling conditions for this hybrid model approach. Based on an Euler implicit discretization, a linear iterative (L-type) domain decomposition scheme is proposed, and proved to be convergent. The theoretical findings are verified by a comparative numerical study that in particular confirms the efficiency of the hybrid ansatz as compared to full two-phase model computations.}, author = {Seus, David and Radu, Florin A. and Rohde, Christian}, doi = {https://doi.org/10.1002/num.22906}, journal = {Numerical Methods for Partial Differential Equations}, number = {n/a}, title = {Towards hybrid two-phase modelling using linear domain decomposition}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22906}, volume = {n/a}, year = 2022 }
  Link
  https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22906
7. Burbulla, S., Hörl, M., & Rohde, C. (2022). Flow in Porous Media with Fractures of Varying Aperture. In arXiv e-prints. https://doi.org/10.48550/arXiv.2207.09301
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  @preprint{burbulla.hoerl.rohde:fractures:2022, abstract = {We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model, where fractures are represented by $(n-1)$-dimensional interfaces between $n$-dimensional subdomains for $n\ge 2$. In particular, we suggest a generalization of the model in~[22] by accounting for asymmetric fractures with spatially varying aperture. Thus, the new model is particularly convenient for the description of surface roughness or for modeling curvilinear or winding fractures. The wellposedness of the new model is proven under appropriate conditions. Further, we formulate a discontinuous Galerkin discretization of the new model and validate the model by performing two- and three-dimensional numerical experiments.}, archiveprefix = {arXiv}, author = {Burbulla, Samuel and Hörl, Maximilian and Rohde, Christian}, doi = {10.48550/arXiv.2207.09301}, eprint = {2207.09301}, eprintclass = {math.NA}, eprinttype = {arXiv}, file = {online:http\:/arxiv.org/pdf/2207.09301:PDF}, journal = {arXiv e-prints}, langid = {english}, primaryclass = {math.NA}, title = {Flow in Porous Media with Fractures of Varying Aperture}, url = {https://doi.org/10.48550/arXiv.2207.09301}, year = 2022 }
  Link
  https://doi.org/10.48550/arXiv.2207.09301
8. Mel’nyk, T., & Rohde, C. (2022). Asymptotic expansion for convection-dominated transport in a thin graph-like junction. In arXiv e-prints. https://doi.org/10.48550/ARXIV.2208.05812
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  @preprint{Melnyk.Rohde:junction:2022], archiveprefix = {arXiv}, author = {Mel'nyk, Taras and Rohde, Christian}, doi = {10.48550/ARXIV.2208.05812}, eprint = {2208.05812}, eprinttype = {arXiv}, journal = {arXiv e-prints}, langid = {english}, primaryclass = {math.AP}, title = {Asymptotic expansion for convection-dominated transport in a thin graph-like junction}, url = {https://arxiv.org/abs/2208.05812}, year = 2022 }
  Link
  https://arxiv.org/abs/2208.05812
9. Burbulla, S., Dedner, A., Hörl, M., & Rohde, C. (2022). Dune-MMesh: The Dune Grid Module for Moving Interfaces. J. Open Source Softw., 7(74), 3959. https://doi.org/10.21105/joss.03959
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  @article{Burbulla2022, author = {Burbulla, Samuel and Dedner, Andreas and Hörl, Maximilian and Rohde, Christian}, doi = {10.21105/joss.03959}, journal = {J. Open Source Softw.}, number = 74, pages = 3959, publisher = {The Open Journal}, title = {Dune-MMesh: The Dune Grid Module for Moving Interfaces}, url = {https://doi.org/10.21105/joss.03959}, volume = 7, year = 2022 }
  Link
  https://doi.org/10.21105/joss.03959
10. Magiera, J., & Rohde, C. (2022). Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics. In K. Schulte, C. Tropea, & B. Weigand (Eds.), Droplet Dynamics under Extreme Ambient Conditions. Springer International Publishing. https://doi.org/10.1007/978-3-031-09008-0_4
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  @inbook{magiera.rohde:analysis:2021, abstract = {The modelling of liquid--vapour flow with phase transition poses many challenges, both on the theoretical level, as well as on the level of discretisation methods. Therefore, accurate mathematical models and efficient numerical methods are required. In that, we focus on two modelling approaches: the sharp-interface (SI) approach and the diffuse-interface (DI) approach. For the SI-approach, representing the phase boundary as a co-dimension-1 manifold, we develop and validate analytical Riemann solvers for basic isothermal two-phase flow scenarios. This ansatz becomes cumbersome for increasingly complex thermodynamical settings. A more versatile multiscale interface solver, that is based on molecular dynamics simulations, is able to accurately describe the evolution of phase boundaries in the temperature-dependent case. It is shown to be even applicable to two-phase flow of multiple components. Despite the successful developments for the SI approach, these models fail if the interface undergoes topological changes. To understand merging and splitting phenomena for droplet ensembles, we consider DI models of second gradient type. For these Navier--Stokes--Korteweg systems, that can be seen as a third order extension of the Navier--Stokes equations, we propose variants that are more accessible to standard numerical schemes. More precisely, we reformulate the capillarity operator to restore the hyperbolicity of the Euler operator in the full system.}, author = {Magiera, Jim and Rohde, Christian}, booktitle = {Droplet Dynamics under Extreme Ambient Conditions}, doi = {10.1007/978-3-031-09008-0_4}, editor = {Schulte, Kathrin and Tropea, Cameron and Weigand, Bernhard}, isbn = {978-3-031-09008-0}, langid = {english}, publisher = {Springer International Publishing}, pubstate = {in review}, series = {Fluid Mechanics and its Application}, title = {Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics}, url = {https://doi.org/10.1007/978-3-031-09008-0_4}, year = 2022 }
  Link
  https://doi.org/10.1007/978-3-031-09008-0_4
2021
1. Alonso-Orán, D., Rohde, C., & Tang, H. (2021). A local-in-time theory for singular SDEs with applications to fluid models with transport noise. J. Nonlinear Sci., 31, Paper No. 98, 55.
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  @article{ORT21, author = {Alonso-Orán, Diego and Rohde, Christian and Tang, Hao}, journal = {J. Nonlinear Sci.}, pages = {Paper No. 98, 55}, title = {A local-in-time theory for singular SDEs with applications to fluid models with transport noise}, volume = 31, year = 2021 }
2. Alkämper, M., Magiera, J., & Rohde, C. (2021). An Interface Preserving Moving Mesh in Multiple SpaceDimensions. Computing Research Repository, abs/2112.11956. https://arxiv.org/abs/2112.11956
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  @article{alkamper2021interface, author = {Alkämper, Maria and Magiera, Jim and Rohde, Christian}, journal = {Computing Research Repository}, title = {An Interface Preserving Moving Mesh in Multiple SpaceDimensions}, url = {https://arxiv.org/abs/2112.11956}, volume = {abs/2112.11956}, year = 2021 }
  Link
  https://arxiv.org/abs/2112.11956
3. Beck, A., Dürrwächter, J., Kuhn, T., Meyer, F., Munz, C.-D., & Rohde, C. (2021). Uncertainty Quantification in High Performance Computational Fluid Dynamics. In W. E. Nagel, D. H. Kröner, & M. M. Resch (Eds.), High Performance Computing in Science and Engineering ’19 (pp. 355--371). Springer International Publishing.
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  @inproceedings{10.1007/978-3-030-66792-4_24, abstract = {In this report we present advances in our research on direct aeroacoustics and uncertainty quantification, based on the high-order Discontinuous Galerkin solver FLEXI. Oscillation phenomena triggered by flow over cavities can lead to an unpleasant tonal (whistling) noise, which provides motivation for industry and academia to better understand the underlying mechanisms. We present a numerical setup capable of capturing these phenomena with high efficiency, as we show by comparison to experimental data and results from industry. Some of these phenomena are highly sensitive towards flow conditions, which makes an integrated approach regarding these conditions necessary. This is the goal of uncertainty quantification. We present software for both intrusive and non-intrusive uncertainty quantification methods. We investigate convergence and computational performance. The development of both codes was in parts carried out in cooperation with HLRS. Apart from validation results, we show a non-intrusive simulation of 3D turbulent cavity noise.}, address = {Cham}, author = {Beck, Andrea and D{\"u}rrw{\"a}chter, Jakob and Kuhn, Thomas and Meyer, Fabian and Munz, Claus-Dieter and Rohde, Christian}, booktitle = {High Performance Computing in Science and Engineering '19}, editor = {Nagel, Wolfgang E. and Kr{\"o}ner, Dietmar H. and Resch, Michael M.}, isbn = {978-3-030-66792-4}, pages = {355--371}, publisher = {Springer International Publishing}, title = {Uncertainty Quantification in High Performance Computational Fluid Dynamics}, year = 2021 }
4. Dürrwächter, J., Meyer, F., Kuhn, T., Beck, A., Munz, C.-D., & Rohde, C. (2021). A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations. Computers & Fluids, 228, 1850044, 20. https://doi.org/10.1016/j.compfluid.2021.105039
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  @article{Duerrwaechter2019, abstract = {We present a Stochastic Galerkin (SG) scheme for Uncertainty Quantification (UQ) of the compressible Navier-Stokes and Euler equations. For spatial discretization, we rely on the high-order Discontinuous Galerkin Spectral Element Method (DGSEM) in combination with an explicit time-stepping scheme. We simulate complex flow problems in two- and three-dimensional domains using curved unstructured hexahedral meshes. The dimension of the stochastic space can be arbitrarily large. In order to treat discontinuities and to ensure hyperbolicity, we employ a multi-element approach in combination with a hyperbolicity-preserving limiter in the stochastic domain and a Finite Volume subcell shock capturing scheme in physical space. Special emphasis is put on code performance and massive parallel scalability. We demonstrate the versatility and broad applicability of our code with various numerical experiments including the supersonic flow around a spacecraft geometry. By this, we wish to contribute to the path of the Stochastic Galerkin method towards practical applicability in research and industrial engineering.}, author = {D{\"u}rrw{\"a}chter, Jakob and Meyer, Fabian and Kuhn, Thomas and Beck, Andrea and Munz, Claus-Dieter and Rohde, Christian}, doi = {10.1016/j.compfluid.2021.105039}, issn = {0045-7930}, journal = {Computers & Fluids}, pages = {1850044, 20}, title = {A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations}, url = {https://www.researchgate.net/profile/Jakob_Duerrwaechter/publication/336702251_A_High-Order_Stochastic_Galerkin_Code_for_the_Compressible_Euler_and_Navier-Stokes_Equations/links/5dadf498299bf111d4bf8ba1/A-High-Order-Stochastic-Galerkin-Code-for-the-Compressible-Euler-and-Navier-Stokes-Equations.pdf}, volume = 228, year = 2021 }
  Link
  https://www.researchgate.net/profile/Jakob_Duerrwaechter/publication/336702251_A_High-Order_Stochastic_Galerkin_Code_for_the_Compressible_Euler_and_Navier-Stokes_Equations/links/5dadf498299bf111d4bf8ba1/A-High-Order-Stochastic-Galerkin-Code-for-the-Compressible-Euler-and-Navier-Stokes-Equations.pdf
5. von Wolff, L., Weinhardt, F., Class, H., Hommel, J., & Rohde, C. (2021). Investigation of Crystal Growth in Enzymatically Induced Calcite Precipitation by Micro-Fluidic Experimental Methods and Comparison with Mathematical Modeling. Transp. Porous Media, 137(2), 327--343. https://doi.org/10.1007/s11242-021-01560-y
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  @article{MR4231733, author = {von Wolff, Lars and Weinhardt, Felix and Class, Holger and Hommel, Johannes and Rohde, Christian}, doi = {10.1007/s11242-021-01560-y}, fjournal = {Transport in Porous Media}, issn = {0169-3913}, journal = {Transp. Porous Media}, mrnumber = {4231733}, number = 2, pages = {327--343}, title = {Investigation of Crystal Growth in Enzymatically Induced Calcite Precipitation by Micro-Fluidic Experimental Methods and Comparison with Mathematical Modeling}, url = {https://doi.org/10.1007/s11242-021-01560-y}, volume = 137, year = 2021 }
  Link
  https://doi.org/10.1007/s11242-021-01560-y
6. Rohde, C., & von Wolff, L. (2021). A Ternary Cahn-Hilliard-Navier-Stokes model for two phase flow with precipitation and dissolution. Math. Models Methods Appl. Sci., 31(1), 1--35. https://doi.org/10.1142/S0218202521500019
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  @article{MR4216046, author = {Rohde, Christian and von Wolff, Lars}, doi = {10.1142/S0218202521500019}, fjournal = {Mathematical Models and Methods in Applied Sciences}, issn = {0218-2025}, journal = {Math. Models Methods Appl. Sci.}, mrclass = {76D05 (35C20 35Q35 35R35 76D45 76T99)}, mrnumber = {4216046}, number = 1, pages = {1--35}, title = {A Ternary Cahn-Hilliard-Navier-Stokes model for two phase flow with precipitation and dissolution}, url = {https://doi.org/10.1142/S0218202521500019}, volume = 31, year = 2021 }
  Link
  https://doi.org/10.1142/S0218202521500019
7. Miao, Y., Rohde, C., & Tang, H. (2021). Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities. https://arxiv.org/abs/2105.08607
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  @misc{miao2021wellposedness, archiveprefix = {arXiv}, author = {Miao, Yingting and Rohde, Christian and Tang, Hao}, eprint = {2105.08607}, primaryclass = {math.AP}, title = {Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities}, url = {https://arxiv.org/abs/2105.08607}, year = 2021 }
  Link
  https://arxiv.org/abs/2105.08607
8. Giesselmann, J., Meyer, F., & Rohde, C. (2021). Error control for statistical solutions of hyperbolic systems of conservation laws. Calcolo, 58(2), Paper No. 23, 29. https://doi.org/10.1007/s10092-021-00417-6
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  @article{GMR21, author = {Giesselmann, Jan and Meyer, Fabian and Rohde, Christian}, doi = {10.1007/s10092-021-00417-6}, journal = {Calcolo}, number = 2, pages = {Paper No. 23, 29}, title = {Error control for statistical solutions of hyperbolic systems of conservation laws}, url = {https://doi.org/10.1007/s10092-021-00417-6}, volume = 58, year = 2021 }
  Link
  https://doi.org/10.1007/s10092-021-00417-6
9. Rohde, C., & Tang, H. (2021). On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena. NoDEA Nonlinear Differential Equations Appl., 28(1), Paper No. 5, 34. https://doi.org/10.1007/s00030-020-00661-9
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  @article{MR4192427, author = {Rohde, Christian and Tang, Hao}, doi = {10.1007/s00030-020-00661-9}, fjournal = {NoDEA. Nonlinear Differential Equations and Applications}, issn = {1021-9722}, journal = {NoDEA Nonlinear Differential Equations Appl.}, mrclass = {60H15 (35A01 35B44 35Q51)}, mrnumber = {4192427}, number = 1, pages = {Paper No. 5, 34}, title = {On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena}, url = {https://doi.org/10.1007/s00030-020-00661-9}, volume = 28, year = 2021 }
  Link
  https://doi.org/10.1007/s00030-020-00661-9
10. Rohde, C., & Tang, H. (2021). On a stochastic Camassa-Holm type equation with higher order nonlinearities. J. Dynam. Differential Equations, 33, 1823–1852. https://doi.org/10.1007/s10884-020-09872-1
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  @article{rohde2020stochastic, archiveprefix = {arXiv}, author = {Rohde, Christian and Tang, Hao}, doi = {https://doi.org/10.1007/s10884-020-09872-1}, eprint = {2001.05754}, journal = {J. Dynam. Differential Equations}, pages = {1823–1852}, primaryclass = {math.AP}, title = {On a stochastic Camassa-Holm type equation with higher order nonlinearities}, volume = 33, year = 2021 }
11. Gander, M., Lunowa, S., & Rohde, C. (2021). Consistent and asymptotic-preserving finite-volume domain decomposition methods for singularly perturbed elliptic equations. Domain Decomposition Methods in Science and Engineering XXVI. http://www.uhasselt.be/Documents/CMAT/Preprints/2021/UP2103.pdf
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  @inproceedings{GanderLunowaRohde2021, author = {Gander, Martin and Lunowa, Stephan and Rohde, Christian}, booktitle = {Domain Decomposition Methods in Science and Engineering XXVI}, publisher = {Lect. Notes Comput. Sci. Eng., Springer, Cham }, title = {Consistent and asymptotic-preserving finite-volume domain decomposition methods for singularly perturbed elliptic equations}, url = {http://www.uhasselt.be/Documents/CMAT/Preprints/2021/UP2103.pdf}, year = 2021 }
  Link
  http://www.uhasselt.be/Documents/CMAT/Preprints/2021/UP2103.pdf
2020
1. Ostrowski, L., & Rohde, C. (2020). Compressible multicomponent flow in porous media with Maxwell-Stefan diffusion. Math. Meth. Appl. Sci., 43(7), 4200–4221. https://doi.org/10.1002/mma.6185
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  @article{OstrowskiRohde2020, abstract = {We introduce a Darcy‐scale model to describe compressible multicomponent flow in a fully saturated porous medium. In order to capture cross‐diffusive effects between the different species correctly, we make use of the Maxwell–Stefan theory in a thermodynamically consistent way. For inviscid flow, the model turns out to be a nonlinear system of hyperbolic balance laws. We show that the dissipative structure of the Maxwell‐Stefan operator permits to guarantee the existence of global classical solutions for initial data close to equilibria. Furthermore, it is proven by relative entropy techniques that solutions of the Darcy‐scale model tend in a certain long‐time regime to solutions of a parabolic limit system.}, author = {Ostrowski, Lukas and Rohde, Christian}, doi = {10.1002/mma.6185}, journal = {Math. Meth. Appl. Sci. }, number = 7, pages = {4200-4221}, title = {Compressible multicomponent flow in porous media with Maxwell-Stefan diffusion}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.6185}, volume = 43, year = 2020 }
  Link
  https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.6185
2. Magiera, J., Ray, D., Hesthaven, J. S., & Rohde, C. (2020). Constraint-aware neural networks for Riemann problems. J. Comput. Phys., 409(109345), Article 109345. https://doi.org/10.1016/j.jcp.2020.109345
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  @article{magiera2019constraintaware, abstract = {Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtain reliable results. However, standard machine learning algorithms are generally not tailored to respect such constraints. We propose two different strategies to generate constraint-aware neural networks. We test their performance in the context of front-capturing schemes for strongly nonlinear wave motion in compressible fluid flow. Precisely in this context so-called Riemann problems have to be solved as surrogates. Their solution describes the local dynamics of the captured wave front in numerical simulations. Three model problems are considered: a cubic flux model problem, an isothermal two-phase flow model, and the Euler equations. We observe, that constraint-aware neural networks do not only account for the constraint but lead to an improvement of the numerical accuracy of the overall fluid simulation.}, author = {Magiera, Jim and Ray, Deep and Hesthaven, Jan S. and Rohde, Christian}, doi = {https://doi.org/10.1016/j.jcp.2020.109345}, issn = {0021-9991}, journal = {J. Comput. Phys.}, number = 109345, title = {Constraint-aware neural networks for Riemann problems}, url = {https://doi.org/10.1016/j.jcp.2020.109345}, volume = 409, year = 2020 }
  Link
  https://doi.org/10.1016/j.jcp.2020.109345
3. Giesselmann, J., Meyer, F., & Rohde, C. (2020). A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method. IMA J. Numer. Anal., 40(2), 1094–1121. https://doi.org/10.1093/imanum/drz004
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  @article{Meyeretal20a, abstract = {In this article we present an a posteriori error estimator for the spatial-stochastic error of a Galerkin-type discretisation of an initial value problem for a random hyperbolic conservation law. For the stochastic discretisation we use the Stochastic Galerkin method and for the spatial-temporal discretisation of the Stochastic Galerkin system a Runge-Kutta Discontinuous Galerkin method. The estimator is obtained using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework of Dafermos \cite{dafermos2005hyperbolic}, this leads to computable error bounds for the space-stochastic discretisation error. \\ Moreover, it turns out that the error estimator admits a splitting into one part representing the spatial error, and a remaining term, which can be interpreted as the stochastic error. This decomposition allows us to balance the errors arising from spatial and stochastic discretisation. We conclude with some numerical examples confirming the theoretical findings. }, author = {Giesselmann, J. and Meyer, F. and Rohde, C.}, doi = {10.1093/imanum/drz004}, issn = {0272-4979}, journal = {IMA J. Numer. Anal.}, mrnumber = {4092280}, number = 2, pages = {1094-1121}, title = {A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method}, url = {https://doi.org/10.1093/imanum/drz004}, volume = 40, year = 2020 }
  Link
  https://doi.org/10.1093/imanum/drz004
4. Rohde, C., & von Wolff, L. (2020). Homogenization of non-local Navier-Stokes-Korteweg equations for compressible liquid-vapour flow in porous media. SIAM J. Math. Anal., 52(6), 6155–6179. https://doi.org/10.1137/19M1242434
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  @article{rohdevwolff20, author = {Rohde, Christian and von Wolff, Lars}, doi = {10.1137/19M1242434}, issn = {0036-1410}, journal = {SIAM J. Math. Anal.}, mrclass = {76M50 (76N99 76T10)}, mrnumber = {4182904}, number = 6, pages = {6155-6179}, title = {Homogenization of non-local Navier-Stokes-Korteweg equations for compressible liquid-vapour flow in porous media}, url = {https://doi.org/10.1137/19M1242434}, volume = 52, year = 2020 }
  Link
  https://doi.org/10.1137/19M1242434
5. Giesselmann, J., Meyer, F., & Rohde, C. (2020). An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws. In A. Bressan, M. Lewicka, D. Wang, & Y. Zheng (Eds.), Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018 (Vol. 10, pp. 449–456). AIMS Series on Applied Mathematics. https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf
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  @inproceedings{GiesselmannMeyerRohdeNISP19, abstract = {We present an a posteriori error analysis for one-dimensional ran-dom hyperbolic systems of conservation laws. For the discretization of therandom space we consider the Non-Intrusive Spectral Projection method, thespatio-temporal discretization uses the Runge–Kutta Discontinuous Galerkinmethod. We derive an a posteriori error estimator using smooth reconstructionsof the numerical solution, which combined with the relative entropy stabilityframework yields computable error bounds for the space-stochastic discretiza-tion error. Moreover, we show that the estimator admits a splitting into astochastic and deterministic part.}, author = {Giesselmann, J. and Meyer, F. and Rohde, C.}, booktitle = {Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018}, editor = {Bressan, Alberto and Lewicka, Marta and Wang, Dehua and Zheng, Yuxi}, owner = {meyerfn}, pages = {449-456}, publisher = {AIMS Series on Applied Mathematics}, title = {An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws}, url = {https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf}, volume = 10, year = 2020 }
  Link
  https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf
6. Giesselmann, J., Meyer, F., & Rohde, C. (2020). A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws. BIT Numerical Mathematics, 60(3), 619–649. https://doi.org/10.1007/s10543-019-00794-z
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  BibTeX
  @article{giesselmann2020, abstract = {This article considers one-dimensional random systems of hyperbolic conservation laws. Existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws, which involve random initial data and random flux functions, are established. Based on these results an a posteriori error analysis for a numerical approximation of the random entropy solution is presented. For the stochastic discretization, a non-intrusive approach, namely the Stochastic Collocation method is used. The spatio-temporal discretization relies on the Runge–Kutta Discontinuous Galerkin method. The a posteriori estimator is derived using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. The scaling properties of the residuals are investigated and the efficiency of the proposed adaptive algorithms is illustrated in various numerical examples.}, author = {Giesselmann, Jan and Meyer, Fabian and Rohde, Christian}, doi = {10.1007/s10543-019-00794-z}, issn = {15729125}, journal = {BIT Numerical Mathematics}, number = 3, pages = {619-649}, refid = {Giesselmann2020}, title = {A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws}, volume = 60, year = 2020 }
7. Beck, A., Dürrwächter, J., Kuhn, T., Meyer, F., Munz, C.-D., & Rohde, C. (2020). $hp$-Multilevel Monte Carlo methods for uncertainty quantification of compressible flows. SIAM J. Sci. Comput., 42(4), B1067–B1091. https://doi.org/10.1137/18M1210575
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  @article{meyeretal2020, abstract = {We propose a novel $hp$-Multilevel Monte Carlo method for the quantification of uncertainties in compressible flows using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits hierarchies of uniformly refined meshes jointly with an increasing polynomial degree for the ansatz space. It allows for a very large range of resolutions in the physical space and thus an efficient decrease of the statistical error. We prove that the overall complexity of the $hp$-Multilevel Monte Carlo method to compute the mean field with prescribed accuracy is of quadratic order with respect to the accuracy. We also propose a novel and simple approach to estimate a lower confidence bound for the optimal number of samples per level, which helps to prevent overshooting the optimal number of samples. The method is in particular adapted to the needs of high-performance computing. Our theoretical results are verified by numerical experiments for the two dimensional compressible Navier-Stokes equations. In particular we consider a cavity flow problem from computational acoustics, demonstrating that the method is suitable to handle complex engineering problems.}, author = {Beck, A. and D\"{u}rrw\"{a}chter, J. and Kuhn, T. and Meyer, F. and Munz, C.-D. and Rohde, C.}, doi = {https://doi.org/10.1137/18M1210575}, journal = {SIAM J. Sci. Comput.}, number = 4, owner = {meyerfn}, pages = {B1067–B1091}, title = {$hp$-Multilevel Monte Carlo methods for uncertainty quantification of compressible flows}, url = {https://arxiv.org/abs/1808.10626}, volume = 42, year = 2020 }
  Link
  https://arxiv.org/abs/1808.10626
8. Armiti-Juber, A., & Rohde, C. (2020). On the well-posedness of a nonlinear fourth-order extension of Richards’ equation. J. Math. Anal. Appl., 487(2), 124005. https://doi.org/10.1016/j.jmaa.2020.124005
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  @article{ARMITIJUBER2020124005, abstract = {We study a nonlinear fourth-order extension of Richards' equation that describes infiltration processes in unsaturated soils. We prove the well-posedness of the fourth-order equation by first applying Kirchhoff's transformation to linearize the higher-order terms. The transformed equation is then discretized in time and space and a set of a priori estimates is established. These allow, by means of compactness theorems, extracting a unique weak solution. Finally, we use the inverse of Kirchhoff's transformation to prove the well-posedness of the original equation.}, author = {Armiti-Juber, Alaa and Rohde, Christian}, doi = {https://doi.org/10.1016/j.jmaa.2020.124005}, issn = {0022-247X}, journal = {J. Math. Anal. Appl.}, number = 2, pages = 124005, title = {On the well-posedness of a nonlinear fourth-order extension of Richards' equation}, url = {http://www.sciencedirect.com/science/article/pii/S0022247X20301670}, volume = 487, year = 2020 }
  Link
  http://www.sciencedirect.com/science/article/pii/S0022247X20301670
9. Ostrowski, L., Massa, F. C., & Rohde, C. (2020). A phase field approach to compressible droplet impingement. In G. Lamanna, S. Tonini, G. E. Cossali, & B. Weigand (Eds.), Droplet Interactions and Spray Processes (pp. 113–126). Springer International Publishing. https://doi.org/10.1007/978-3-030-33338-6_9
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  @inproceedings{10.1007/978-3-030-33338-6_9, abstract = {We consider the impingement of a droplet onto a wall with high impact speed. To model this process we favour a diffuse-interface concept. Precisely, we suggest a compressible Navier--Stokes--Allen--Cahn model following [5]. Basic properties of the model are discussed. To cope with the fluid-wall interaction, we derive thermodynamically consistent boundary conditions that account for dynamic contact angles. We briefly discuss a discontinuous Galerkin scheme which approximates the energy dissipation of the system exactly and illustrate the results with a series of numerical simulations. Currently, these simulations are restricted to static contact angle boundary conditions.}, address = {Cham}, author = {Ostrowski, Lukas and Massa, F. C. and Rohde, Christian}, booktitle = {Droplet Interactions and Spray Processes}, editor = {Lamanna, G. and Tonini, S. and Cossali, G. E. and Weigand, B.}, isbn = {978-3-030-33338-6}, pages = {113-126}, publisher = {Springer International Publishing}, title = {A phase field approach to compressible droplet impingement}, url = {https://doi.org/10.1007/978-3-030-33338-6_9}, year = 2020 }
  Link
  https://doi.org/10.1007/978-3-030-33338-6_9
10. Burbulla, S., & Rohde, C. (2020). A fully conforming finite volume approach to two-phase flow in fractured porous media. In R. Klöfkorn, E. Keilegavlen, F. A. Radu, & J. Fuhrmann (Eds.), Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (pp. 547–555). Springer International Publishing. https://doi.org/10.1007/978-3-030-43651-3_51
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  @inproceedings{Burbulla2020, abstract = {In many natural and technical applications in porous media fluid's flow behavior is highly affected by fractures. Many approaches employ mixed-dimensional models that model thin features as dimension-reduced manifolds. Following this idea, we consider porous media where dominant heterogeneities are geometrically represented by sharp interfaces. We model incompressible two-phase flow in porous media both in the bulk porous medium and within the fractures. We present a reliable and geometrically flexible implementation of a fully conforming finite volume approach within the DUNE framework for two and three spatial dimensions. The implementation is based on the new dune-mmesh grid implementation that manages bulk and surface triangulation simultaneously. The model and the implementation are extended to handle fracture junctions. We apply our scheme to benchmark cases with complex fracture networks to show the reliability of the approach.}, address = {Cham}, author = {Burbulla, Samuel and Rohde, Christian}, booktitle = {Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples}, doi = {https://doi.org/10.1007/978-3-030-43651-3_51}, editor = {Klöfkorn, Robert and Keilegavlen, Eirik and Radu, Florin A. and Fuhrmann, Jürgen}, pages = {547-555}, publisher = {Springer International Publishing}, title = {A fully conforming finite volume approach to two-phase flow in fractured porous media}, url = {https://link.springer.com/chapter/10.1007%2F978-3-030-43651-3_51}, year = 2020 }
  Link
  https://link.springer.com/chapter/10.1007%2F978-3-030-43651-3_51
11. Ostrowski, L., & Rohde, C. (2020). Phase field modelling for compressible droplet impingement. In A. Bressan, M. Lewicka, D. Wang, & Y. Zheng (Eds.), Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018 (Vol. 10, pp. 586–593). AIMS Series on Applied Mathematics. https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf
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  BibTeX
  @inproceedings{ostrowski2020phase, abstract = {We consider the impingement of a droplet onto a wall with high im-pact speed. For this purpose an isothermal Navier–Stokes–Allen–Cahn model[5] is used. Properties of the model are discussed. In order to solve the systemnumerically we introduce an energy consistent discontinuous Galerkin schemeand show a numerical example of droplet impact.}, author = {Ostrowski, Lukas and Rohde, Christian}, booktitle = {Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018}, editor = {Bressan, Alberto and Lewicka, Marta and Wang, Dehua and Zheng, Yuxi}, pages = {586-593}, publisher = {AIMS Series on Applied Mathematics}, title = {Phase field modelling for compressible droplet impingement }, url = {https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf}, volume = 10, year = 2020 }
  Link
  https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf
12. Hitz, T., Keim, J., Munz, C.-D., & Rohde, C. (2020). A parabolic relaxation model for the Navier-Stokes-Korteweg equations. J. Comput. Phys., 421, 109714. https://doi.org/10.1016/j.jcp.2020.109714
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  @article{HITZ2020109714, abstract = {The isothermal Navier-Stokes-Korteweg system is a classical diffuse interface model for compressible two-phase flow which grounds in Van Der Waals' theory of capillarity. However, the numerical solution faces two major challenges: due to a third-order dispersion contribution in the momentum equations, extended numerical stencils are required for the flux calculation. Furthermore, the equation of state given by a Van-der-Waals law, exhibits non-monotone behaviour in the two-phase state space leading to imaginary eigenvalues of the Jacobian of the first-order fluxes. In this work a lower-order parabolic relaxation model is used to approximate solutions of the classical NSK equations. Whereas an additional parabolic evolution equation for the relaxation variable has to be solved, the system involves no differential operator of higher as second order. The use of a modified pressure function guarantees that the first-order fluxes remain hyperbolic. Altogether, the relaxation system is directly accessible for standard compressible flow solvers. We use the higher-order Discontinuous Galerkin spectral element method as realized in the open source code FLEXI. The relaxation model is validated against solutions of the original NSK model for a variety of 1D and 2D test cases. Three-dimensional simulations of head-on droplet collisions for a range of different collision Weber numbers underline the capability of the approach.}, author = {Hitz, Timon and Keim, Jens and Munz, Claus-Dieter and Rohde, Christian}, doi = {https://doi.org/10.1016/j.jcp.2020.109714}, issn = {0021-9991}, journal = {J. Comput. Phys.}, pages = 109714, title = {A parabolic relaxation model for the Navier-Stokes-Korteweg equations}, url = {http://www.sciencedirect.com/science/article/pii/S0021999120304885}, volume = 421, year = 2020 }
  Link
  http://www.sciencedirect.com/science/article/pii/S0021999120304885
2019
1. Colombo, R. M., LeFloch, P. G., Rohde, C., & Trivisa, K. (2019). Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics. Oberwohlfach Rep., 16, 1419–1497. https://www.ems-ph.org/journals/show_issue.php?issn=1660-8933&vol=16&iss=2
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  @article{CLRT_MFO2019, author = {Colombo, R. M. and LeFloch, P. G. and Rohde, C. and Trivisa, K.}, journal = {Oberwohlfach Rep.}, note = {Abstracts from the workshop held June 19--25, 2016, Organized by Rinaldo M. Colombo, Philippe G. LeFloch and Christian Rohde}, number = 16, pages = {1419-1497}, title = {Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics}, url = {https://www.ems-ph.org/journals/show_issue.php?issn=1660-8933&vol=16&iss=2}, year = 2019 }
  Link
  https://www.ems-ph.org/journals/show_issue.php?issn=1660-8933&vol=16&iss=2
2. Kuhn, T., Dürrwächter, J., Meyer, F., Beck, A., Rohde, C., & Munz, C.-D. (2019). Uncertainty quantification for direct aeroacoustic simulations of cavity flows. J. Theor. Comput. Acoust., 27(1), 1850044, 20. https://doi.org/10.1142/S2591728518500445
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  @article{kuhn2018uncertainty, abstract = {We investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows. The so-called Rossiter feedback requires a direct numerical computation of the acoustic noise, which solves hydrodynamics and acoustics simultaneously, in order to capture the interaction of acoustic waves and the hydrodynamics of the flow. Due to the large bandwidth of spatial and temporal scales, a high order numerical scheme with low dissipation and dispersion error is necessary to preserve important small scale information. Therefore, the open-source CFD solver FLEXI, which is based on a high-order discontinuous Galerkin spectral element method, is used to perform the aforementioned direct simulations of an open cavity configuration with a laminar upstream boundary layer. To analyse the precision of the deterministic cavity simulation with respect to random input parameters we establish a framework for uncertainty quantification. In particular, a non-intrusive spectral projection method with Legendre and Hermite polynomial basis functions is employed in order to treat uniform and normal probability distributions of the uncertain input. The results indicate a strong, non-linear dependency of the acoustic feedback mechanism on the investigated uncertain input parameters. An analysis of the stochastic results offers new insights into the noise generation process of open cavity flows and reveals the strength of the implemented uncertainty quantification framework.}, author = {Kuhn, Thomas and Dürrwächter, Jakob and Meyer, Fabian and Beck, Andrea and Rohde, Christian and Munz, Claus-Dieter}, doi = {https://doi.org/10.1142/S2591728518500445}, issn = {{2591-7811} and {2591-7285}}, journal = {J. Theor. Comput. Acoust.}, journalsubtitle = {an IMACS journal}, journaltitle = {Journal of theoretical and computational acoustics}, language = {eng}, number = 1, pages = {1850044, 20}, title = {Uncertainty quantification for direct aeroacoustic simulations of cavity flows}, url = {https://doi.org/10.1142/S2591728518500445}, volume = 27, year = 2019 }
  Link
  https://doi.org/10.1142/S2591728518500445
3. Sharanya, V., Sekhar, G. P. R., & Rohde, C. (2019). Surfactant-induced migration of a spherical droplet in non-isothermal Stokes flow. Physics of Fluids, 31(1), 012110. https://doi.org/10.1063/1.5064694
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  @article{sharanya2019surfactantinduced, author = {Sharanya, V. and Sekhar, G.P. Raja and Rohde, Christian}, doi = {10.1063/1.5064694}, journal = {Physics of Fluids}, number = 1, pages = 012110, title = {Surfactant-induced migration of a spherical droplet in non-isothermal Stokes flow}, url = {https://doi.org/10.1063/1.5064694}, volume = 31, year = 2019 }
  Link
  https://doi.org/10.1063/1.5064694
4. Armiti-Juber, A., & Rohde, C. (2019). On Darcy-and Brinkman-type models for two-phase flow in asymptotically flat domains. Comput. Geosci., 23(2), 285–303. https://doi.org/10.1007/s10596-018-9756-2
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  @article{armitijuber2017darcyand, author = {Armiti-Juber, A. and Rohde, C.}, doi = {https://doi.org/10.1007/s10596-018-9756-2}, journal = {Comput. Geosci.}, number = 2, owner = {seusdd}, pages = {285-303}, publisher = {Springer International Publishing}, title = {On Darcy-and Brinkman-type models for two-phase flow in asymptotically flat domains}, url = {https://link.springer.com/article/10.1007/s10596-018-9756-2}, volume = 23, year = 2019 }
  Link
  https://link.springer.com/article/10.1007/s10596-018-9756-2
5. Armiti-Juber, A., & Rohde, C. (2019). Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media. J. Math. Anal. Appl., 477(1), 592–612. https://doi.org/10.1016/j.jmaa.2019.04.049
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  @article{armitit2019existence, author = {Armiti-Juber, Alaa and Rohde, Christian}, doi = {https://doi.org/10.1016/j.jmaa.2019.04.049}, journal = {J. Math. Anal. Appl.}, language = {eng}, number = 1, pages = {592-612}, title = {Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media}, volume = 477, year = 2019 }
6. Seus, D., Radu, F. A., & Rohde, C. (2019). A linear domain decomposition method for two-phase flow in porous media. Numerical Mathematics and Advanced Applications ENUMATH 2017, 603–614. https://doi.org/10.1007/978-3-319-96415-7_55
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  BibTeX
  @inproceedings{seus2017linear, author = {Seus, David and Radu, Florin A. and Rohde, Christian}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2017}, doi = {10.1007/978-3-319-96415-7_55}, isbn = {978-3-319-96415-7}, owner = {seusdd}, pages = {603-614}, publisher = {Springer International Publishing}, title = {A linear domain decomposition method for two-phase flow in porous media}, year = 2019 }
7. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Santin, G., Wittwar, D., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., & Rohde, C. (2019). Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario. Computational Geosciences, 23(2), 339--354. https://doi.org/10.1007/s10596-018-9785-x
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  BibTeX
  @article{Koeppel2018, abstract = {A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of parameters in constitutive relations, and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitrary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation, and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally, we offer suggestions about the methods' advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.}, author = {K{\"o}ppel, Markus and Franzelin, Fabian and Kr{\"o}ker, Ilja and Oladyshkin, Sergey and Santin, Gabriele and Wittwar, Dominik and Barth, Andrea and Haasdonk, Bernard and Nowak, Wolfgang and Pfl{\"u}ger, Dirk and Rohde, Christian}, day = 01, doi = {10.1007/s10596-018-9785-x}, issn = {1573-1499}, journal = {Computational Geosciences}, month = {04}, number = 2, pages = {339--354}, title = {Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario}, url = {https://doi.org/10.1007/s10596-018-9785-x}, volume = 23, year = 2019 }
  Link
  https://doi.org/10.1007/s10596-018-9785-x
2018
1. Raja Sekhar, G. P., Sharanya, V., & Rohde, C. (2018). Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number. International Journal of Multiphase Flow, 107, 82–103. http://arxiv.org/abs/1609.03410
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  @article{rajasekhar2018effect, abstract = {The motion of a viscous drop is investigated when the interface is fully covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes flow for the low surface P\'eclet number limit. The effect of the interfacial slip coefficient on the behavior of the flow field is also considered. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen's laws using a perturbation ansatz in powers of the surface P\'eclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surface P\'eclet number. Further instances corresponding to a given ambient flow as uniform flow, Couette flow, Poiseuille flow are analyzed. Moreover, it is observed that, a surfactant-induced cross-stream migration of the drop occur towards the centre-line in both Couette flow and Poiseuille flow cases. The variation of the drag force and migration velocity is computed for different parameters such as P\'eclet number, Marangoni number etc.}, author = {Raja Sekhar, G. P. and Sharanya, V. and Rohde, Christian}, journal = {International Journal of Multiphase Flow}, owner = {szur}, pages = {82-103}, title = {Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number}, url = {http://arxiv.org/abs/1609.03410}, volume = 107, year = 2018 }
  Link
  http://arxiv.org/abs/1609.03410
2. Seus, D., Pop, I. S., Rohde, C., Mitra, K., & Radu, F. (2018). A linear domain decompostition method for partially saturated flow in porous media. Comput. Methods Appl. Mech. Eng., 333, 331–355. https://doi.org/10.1016/j.cma.2018.01.029
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  BibTeX
  @article{seus2018linear, author = {Seus, David and Pop, Iuliu S. and Rohde, Christian and Mitra, K. and Radu, Florin}, doi = {https://doi.org/10.1016/j.cma.2018.01.029}, journal = {Comput. Methods Appl. Mech. Eng.}, pages = {331-355}, title = {A linear domain decompostition method for partially saturated flow in porous media}, url = {https://doi.org/10.1016/j.cma.2018.01.029}, volume = 333, year = 2018 }
  Link
  https://doi.org/10.1016/j.cma.2018.01.029
3. Fechter, S., Munz, C.-D., Rohde, C., & Zeiler, C. (2018). Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension. Comput. & Fluids, 169, 169–185. http://dx.doi.org/10.1016/j.compfluid.2017.03.026
  - BibTeX
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  BibTeX
  @article{fechter2018approximate, author = {Fechter, Stefan and Munz, Claus-Dieter and Rohde, Christian and Zeiler, Christoph}, doi = {http://dx.doi.org/10.1016/j.compfluid.2017.03.026}, journal = {Comput. \& Fluids}, owner = {szur}, pages = {169-185}, title = {Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension}, url = {http://www.sciencedirect.com/science/article/pii/S004579301730107X}, volume = 169, year = 2018 }
  Link
  http://www.sciencedirect.com/science/article/pii/S004579301730107X
4. Sharanya, V., Sekhar, G. P. R., & Rohde, C. (2018). The low surface Péclet number regime for surfactant-laden viscous droplets: Influence of surfactant concentration, interfacial slip effects and cross migration. Int. J. of Multiph. Flow, 107, 82–103. https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.008
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  BibTeX
  @article{SHARANYA201882, abstract = {We consider the motion of a viscous drop in an arbitrary unsteady Stokes flow such that the surface of the drop is fully covered with a stagnant surfactant layer. In particular the regime of low surface Péclet number is analyzed and we account for the effect interfacial slip on the overall behavior of the flow field. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen’s laws, using a perturbation ansatz in powers of the surface Péclet number. The surface equation of the deformed sphere has been determined by an iterative method up to the first order approximation. Analytical expressions for the migration velocity of the drop are likewise given. Based on this analysis we can completely characterize various flow situations including a given ambient flow as uniform flow, Couette flow and Poiseuille flow. Moreover, we find out that a surfactant-induced cross-stream migration of the drop occurs towards the center-line in both, Couette and Poiseuille flow cases. The variation of the drag force and the migration velocity is computed for different parameters such as the Péclet number and the Marangoni number. Finally, the theoretical findings are validated on with available experimental data.}, author = {Sharanya, V. and Sekhar, G.P. Raja and Rohde, Christian}, doi = {https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.008}, issn = {0301-9322}, journal = {Int. J. of Multiph. Flow}, pages = {82 - 103}, title = {The low surface Péclet number regime for surfactant-laden viscous droplets: Influence of surfactant concentration, interfacial slip effects and cross migration}, url = {http://www.sciencedirect.com/science/article/pii/S0301932217306675}, volume = 107, year = 2018 }
  Link
  http://www.sciencedirect.com/science/article/pii/S0301932217306675
5. Rohde, C., & Zeiler, C. (2018). On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension. Z. Angew. Math. Phys., 3, 69, Art. 76. https://doi.org/10.1007/s00033-018-0958-1
  - BibTeX
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  BibTeX
  @article{rohde2018riemann, author = {Rohde, C. and Zeiler, C.}, doi = {https://doi.org/10.1007/s00033-018-0958-1}, journal = {Z. Angew. Math. Phys.}, number = 3, owner = {szur}, pages = {69, Art. 76}, title = {On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension}, url = {https://doi.org/10.1007/s00033-018-0958-1}, year = 2018 }
  Link
  https://doi.org/10.1007/s00033-018-0958-1
6. Chalons, C., Magiera, J., Rohde, C., & Wiebe, M. (2018). A finite-volume tracking scheme for two-phase compressible flow. Springer Proc. Math. Stat., 309--322. https://doi.org/10.1007/978-3-319-91545-6_25
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  BibTeX
  @article{chalons.magiera.ea:finite:2018, abstract = {We propose a finite-volume tracking method in multiple space dimensions to approximate weak solutions of the hydromechanical equations that allow two-phase behavior. The method relies on a moving mesh ansatz such that the phase boundary is represented as a sharp interface without any artificial smearing. At the interface, an approximate solver is applied, such that the exact Riemann solution is not required. From precedent work, it is known that the method is locally conservative and recovers planar traveling wave solutions exactly. To demonstrate the efficiency and reliability of the new scheme, we test it on various situations for liquid--vapor flow.}, address = {Cham}, author = {Chalons, Christophe and Magiera, Jim and Rohde, Christian and Wiebe, Maria}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, doi = {https://doi.org/10.1007/978-3-319-91545-6_25}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, isbn = {978-3-319-91545-6}, journal = {Springer Proc. Math. Stat.}, pages = {309--322}, publisher = {Springer International Publishing}, title = {A finite-volume tracking scheme for two-phase compressible flow}, url = {https://doi.org/10.1007/978-3-319-91545-6_25}, year = 2018 }
  Link
  https://doi.org/10.1007/978-3-319-91545-6_25
7. Seus, D., Mitra, K., Pop, I. S., Radu, F. A., & Rohde, C. (2018). A linear domain decomposition method for partially saturated flow in porous media. Comp. Methods Appl. Mech. Eng., 333, 331--355. https://doi.org/10.1016/j.cma.2018.01.029
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  BibTeX
  @article{seus2018linear, abstract = {Abstract The Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface G . This leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at G . After an Euler implicit discretisation of the resulting nonlinear subproblems, a linear iterative ( L -type) domain decomposition scheme is proposed. The convergence of the scheme is proved rigorously. In the last part we present numerical results that are in line with the theoretical finding, in particular the convergence of the scheme under mild restrictions on the time step size. We further compare the scheme to other approaches not making use of a domain decomposition. Namely, we compare to a Newton and a Picard scheme. We show that the proposed scheme is more stable than the Newton scheme while remaining comparable in computational time, even if no parallelisation is being adopted. After presenting a parametric study that can be used to optimise the proposed scheme, we briefly discuss the effect of parallelisation and give an example of a four-domain implementation.}, author = {Seus, David and Mitra, Koondanibha and Pop, Iuliu Sorin and Radu, Florin Adrian and Rohde, Christian}, doi = {https://doi.org/10.1016/j.cma.2018.01.029}, issn = {0045-7825}, journal = {Comp. Methods Appl. Mech. Eng.}, owner = {seusdd}, pages = {331--355}, title = {A linear domain decomposition method for partially saturated flow in porous media }, url = {https://www.sciencedirect.com/science/article/pii/S0045782518300318}, volume = 333, year = 2018 }
  Link
  https://www.sciencedirect.com/science/article/pii/S0045782518300318
8. Rohde, C. (2018). Fully resolved compressible two-phase flow : modelling, analytical and numerical issues. In M. Bulicek, E. Feireisl, & M. Pokorný (Eds.), New trends and results in mathematical description of fluid flows (pp. 115–181). Birkhäuser. https://doi.org/10.1007/978-3-319-94343-5
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  BibTeX
  @inbook{rohde2018fully, abstract = {Mathematical models for compressible two-phase flow of homogeneous fluids that occur in a liquid and a vapour phase can be classified as either belonging to the class of sharp interface models or to the class of diffuse interface models. Sharp interface models display the phase boundary as a sharp front separating two bulk model domains while diffuse interface models consist of a single model on the complete domain of interest such that phase boundaries are represented as transition zones. This contribution is devoted to a self-consistent introduction to both model classes.}, author = {Rohde, Christian}, booktitle = {New trends and results in mathematical description of fluid flows}, chapter = 4, doi = {10.1007/978-3-319-94343-5}, editor = {Bulicek, Miroslav and Feireisl, Eduard and Pokorný, Milan}, isbn = {{978-3-319-94343-5} and {978-3-319-94342-8}}, language = {eng}, location = {Basel}, pages = {115-181}, publisher = {Birkhäuser}, series = {Nečas Center Series}, title = {Fully resolved compressible two-phase flow : modelling, analytical and numerical issues}, url = {https://doi.org/10.1007/978-3-319-94343-5_4}, year = 2018 }
  Link
  https://doi.org/10.1007/978-3-319-94343-5_4
9. Magiera, J., & Rohde, C. (2018). A particle-based multiscale solver for compressible liquid-vapor flow. Springer Proc. Math. Stat., 291--304. https://doi.org/10.1007/978-3-319-91548-7_23
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  BibTeX
  @article{magiera.rohde:particle:2018, abstract = {To describe complex flow systems accurately, it is in many cases important to account for the properties of fluid flows on a microscopic scale. In this work, we focus on the description of liquid--vapor flow with a sharp interface between the phases. The local phase dynamics at the interface can be interpreted as a Riemann problem for which we develop a multiscale solver in the spirit of the heterogeneous multiscale method (HMM) [7], using a particle-based microscale model to augment the macroscopic two-phase flow system. The application of a microscale model makes it possible to use the intrinsic properties of the fluid at the microscale, instead of formulating (ad hoc) constitutive relations.}, address = {Cham}, author = {Magiera, Jim and Rohde, Christian}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems II}, doi = {10.1007/978-3-319-91548-7_23}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, isbn = {978-3-319-91548-7}, journal = {Springer Proc. Math. Stat.}, pages = {291--304}, publisher = {Springer International Publishing}, title = {A particle-based multiscale solver for compressible liquid-vapor flow}, url = {http://dx.doi.org/10.1007/978-3-319-91548-7_23}, year = 2018 }
  Link
  http://dx.doi.org/10.1007/978-3-319-91548-7_23
2017
1. Fechter, S., Munz, C.-D., Rohde, C., & Zeiler, C. (2017). A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension. J. Comput. Phys., 336, 347–374. https://doi.org/10.1016/j.jcp.2017.02.001
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  BibTeX
  @article{fechter2017sharp, affiliation = {Zeiler, C (Reprint Author), Univ Stuttgart, Inst Angew Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Fechter, Stefan; Munz, Claus-Dieter, Univ Stuttgart, Inst Aerodynam \& Gasdynam, Pfaffenwaldring 21, D-70569 Stuttgart, Germany. Rohde, Christian; Zeiler, Christoph, Univ Stuttgart, Inst Angew Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, author = {Fechter, Stefan and Munz, Claus-Dieter and Rohde, Christian and Zeiler, Christoph}, da = {2018-02-09}, doi = {10.1016/j.jcp.2017.02.001}, eissn = {1090-2716}, issn = {0021-9991}, journal = {J. Comput. Phys.}, language = {English}, month = {05}, pages = {347-374}, publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE}, research-areas = {Computer Science; Physics}, title = {A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension}, type = {Article}, unique-id = {ISI:000397362800018}, url = {https://doi.org/10.1016/j.jcp.2017.02.001}, volume = 336, year = 2017 }
  Link
  https://doi.org/10.1016/j.jcp.2017.02.001
2. Köppel, M., Kröker, I., & Rohde, C. (2017). Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems Governing Two-Phase Flow in Heterogeneous Porous Media. Comput. Geosci., 21, 807–832. https://doi.org/10.1007/s10596-017-9662-z
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  BibTeX
  @article{koppel2017intrusive, author = {Köppel, Markus and Kröker, Ilja and Rohde, Christian}, doi = {10.1007/s10596-017-9662-z}, journal = {Comput. Geosci.}, owner = {szur}, pages = {807-832}, title = {Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems Governing Two-Phase Flow in Heterogeneous Porous Media}, url = {https://link.springer.com/article/10.1007%2Fs10596-017-9662-z}, volume = 21, year = 2017 }
  Link
  https://link.springer.com/article/10.1007%2Fs10596-017-9662-z
3. Chalons, C., Rohde, C., & Wiebe, M. (2017). A finite volume method for undercompressive shock waves in two space dimensions. ESAIM Math. Model. Numer. Anal., 51(5), 1987–2015. https://doi.org/10.1051/m2an/2017027
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  BibTeX
  @article{chalons2017finite, author = {Chalons, Christophe and Rohde, Christian and Wiebe, Maria}, doi = {https://doi.org/10.1051/m2an/2017027}, journal = {ESAIM Math. Model. Numer. Anal.}, month = {09}, number = 5, owner = {seusdd}, pages = {1987-2015}, title = {A finite volume method for undercompressive shock waves in two space dimensions}, url = {https://www.esaim-m2an.org/component/article?access=doi&doi=10.1051/m2an/2017027}, volume = 51, year = 2017 }
  Link
  https://www.esaim-m2an.org/component/article?access=doi&doi=10.1051/m2an/2017027
4. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Santin, G., Wittwar, D., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., & Rohde, C. (2017). Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario. University of Stuttgart. http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759
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  @techreport{koeppel2017, abstract = {A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methodsâ€™ advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.}, author = {K{\"o}ppel, M. and Franzelin, F. and Kr{\"o}ker, I. and Oladyshkin, S. and Santin, G. and Wittwar, D. and Barth, A. and Haasdonk, Bernard and Nowak, W. and Pfl{\"u}ger, D. and Rohde, C.}, groups = {haasdonk, santin}, institution = {University of Stuttgart}, owner = {santinge}, title = {Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759}, year = 2017 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759
5. Kutter, M., Rohde, C., & Sändig, A.-M. (2017). Well-posedness of a two scale model for liquid phase epitaxy with elasticity. Contin. Mech. Thermodyn., 29(4), 989–1016. https://doi.org/10.1007/s00161-015-0462-1
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  @article{kutter2017wellposedness, author = {Kutter, Michael and Rohde, Christian and S\"andig, Anna-Margarete}, doi = {10.1007/s00161-015-0462-1}, issn = {0935-1175}, journal = {Contin. Mech. Thermodyn.}, number = 4, owner = {seusdd}, pages = {989-1016}, title = {Well-posedness of a two scale model for liquid phase epitaxy with elasticity}, url = {http://dx.doi.org/10.1007/s00161-015-0462-1}, volume = 29, year = 2017 }
  Link
  http://dx.doi.org/10.1007/s00161-015-0462-1
6. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Wittwar, D., Santin, G., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., & Rohde, C. (2017). Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage. https://doi.org/10.5281/zenodo.933827
  - BibTeX
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  BibTeX
  @misc{UQ_comparison_dataset, author = {K{\"o}ppel, Markus and Franzelin, Fabian and Kr{\"o}ker, Ilja and Oladyshkin, Sergey and Wittwar, Dominik and Santin, Gabriele and Barth, Andrea and Haasdonk, Bernard and Nowak, Wolfang and Pfl{\"u}ger, Dirk and Rohde, Christian}, doi = {10.5281/zenodo.933827}, month = {11}, owner = {santinge}, title = {{Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage}}, url = {https://doi.org/10.5281/zenodo.933827}, year = 2017 }
  Link
  https://doi.org/10.5281/zenodo.933827
2016
1. Dumbser, M., Gassner, G., Rohde, C., & Roller, S. (2016). Preface to the special issue ``Recent Advances in Numerical Methods for Hyperbolic Partial Differential Equations’’. Appl. Math. Comput., 272(part 2), 235--236. https://doi.org/10.1016/j.amc.2015.11.023
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  @article{dumbser2016preface, author = {Dumbser, Michael and Gassner, Gregor and Rohde, Christian and Roller, Sabine}, doi = {10.1016/j.amc.2015.11.023}, fjournal = {Applied Mathematics and Computation}, issn = {0096-3003}, journal = {Appl. Math. Comput.}, mrclass = {Preliminary Data}, mrnumber = {3421104}, number = {part 2}, owner = {joosde}, pages = {235--236}, title = {Preface to the special issue ``{R}ecent {A}dvances in {N}umerical {M}ethods for {H}yperbolic {P}artial {D}ifferential {E}quations''}, url = {http://dx.doi.org/10.1016/j.amc.2015.11.023}, volume = 272, year = 2016 }
  Link
  http://dx.doi.org/10.1016/j.amc.2015.11.023
2. Kabil, B., & Rohde, C. (2016). Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension. Math. Meth. Appl. Sci., 39(18), 5409--5426. https://doi.org/10.1002/mma.3926
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  BibTeX
  @article{kabil2016persistence, author = {Kabil, Bugra and Rohde, Christian}, doi = {10.1002/mma.3926}, journal = {Math. Meth. Appl. Sci.}, number = 18, owner = {szur}, pages = {5409--5426}, title = {Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension}, url = {http://dx.doi.org/10.1002/mma.3926}, volume = 39, year = 2016 }
  Link
  http://dx.doi.org/10.1002/mma.3926
3. Magiera, J., Rohde, C., & Rybak, I. (2016). A hyperbolic-elliptic model problem for coupled surface-subsurface flow. Transp. Porous Media, 114, 425–455. https://doi.org/10.1007/S11242-015-0548-Z
  - BibTeX
  BibTeX
  @article{magiera2016hyperbolicelliptic, author = {Magiera, J. and Rohde, C. and Rybak, I.}, doi = {10.1007/S11242-015-0548-Z}, journal = {Transp. Porous Media}, owner = {ingrid}, pages = {425-455}, title = {A hyperbolic-elliptic model problem for coupled surface-subsurface flow}, volume = 114, year = 2016 }
4. Barth, A., Bürger, R., Kröker, I., & Rohde, C. (2016). Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach. Computers & Chemical Engineering, 89, 11-- 26. http://dx.doi.org/10.1016/j.compchemeng.2016.02.016
  - BibTeX
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  BibTeX
  @article{barth2016computational, author = {Barth, Andrea and B\"urger, Raimund and Kr\"oker, Ilja and Rohde, Christian}, doi = {http://dx.doi.org/10.1016/j.compchemeng.2016.02.016}, issn = {0098-1354}, journal = {Computers \& Chemical Engineering }, owner = {seusdd}, pages = {11 -- 26}, title = {Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic {G}alerkin approach}, url = {http://www.sciencedirect.com/science/article/pii/S0098135416300503}, volume = 89, year = 2016 }
  Link
  http://www.sciencedirect.com/science/article/pii/S0098135416300503
5. Sharanya, V., Sekhar, G. P. R., & Rohde, C. (2016). Bed of polydisperse viscous spherical drops under thermocapillary effects. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 67(4), Article 4. https://doi.org/10.1007/s00033-016-0699-y
  - BibTeX
  BibTeX
  @article{sharanya2016polydisperse, affiliation = {Sharanya, V (Reprint Author), Indian Inst Technol, Dept Math, Kharagpur 721302, W Bengal, India. Sharanya, V.; Sekhar, G. P. Raja, Indian Inst Technol, Dept Math, Kharagpur 721302, W Bengal, India. Rohde, Christian, Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, article-number = {101}, author = {Sharanya, V. and Sekhar, G. P. Raja and Rohde, Christian}, da = {2017-07-07}, doi = {10.1007/s00033-016-0699-y}, eissn = {1420-9039}, issn = {0044-2275}, journal = {ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, language = {English}, month = {08}, number = 4, oa = {No}, publisher = {SPRINGER BASEL AG}, research-areas = {Mathematics}, title = {Bed of polydisperse viscous spherical drops under thermocapillary effects}, type = {Article}, unique-id = {ISI:000381410100023}, volume = 67, year = 2016 }
6. Redeker, M., Pop, I. S., & Rohde, C. (2016). Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous Media. IMA J. Appl. Math., 81(5), 898–939. https://doi.org/10.1093/imamat/hxw023
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  @article{redeker2016upscaling, abstract = {We consider a porous medium with a pore space that is completely filled by three different phases: two immiscible fluids (say water and oil) and a solid phase. One fluid phase contains dissolved ions, which can precipitate at the pore boundary to form the solid phase. The reverse process of dissolution, is also possible. Consequently, the solid phase changes in time; its variation is not known a-priori. The second fluid contains no solute and has no interaction with the solid phase. Starting from a standard sharp interface model for the pore-scale dynamics we develop a diffuse interface approach that accounts for the time-dependent spatial distribution of the three species and the overall concentration of the solute. Basic analytical results for this model are presented, including the well posedness of the phase field component of the model. Next we apply matched asymptotic techniques to show that the diffuse interface model converges to the sharp interface one. Further, homogenization is applied to derive a new two-scale model that is valid at the Darcy scale. This leads to a parabolic reaction-diffusion system in a medium with variable, concentration dependent porosity. The diffuse interface approach allows describing the variation in the porosity as phase field type equations at the pore-scale. The last part of the paper presents an efficient numerical scheme to approximate the solution of the two-scale model. This scheme has as starting point the algorithm in [M. Redeker and C. Eck. A fast and accurate adaptive solution strategy for two-scale models with continuous inter-scale dependencies. J. Comput. Phys., 240:268�283, 2013]. After some test cases validating the method, we finally present computations for several realistic scenarios. The results demonstrate the interdependence of the change of the pore structure due to precepitaion/dissolution and the evolution of the Darcy scale concentration of the dissolved particles in the one fluid.}, author = {Redeker, Magnus and Pop, Iuliu Sorin and Rohde, Christian}, doi = {https://doi.org/10.1093/imamat/hxw023}, journal = {IMA J. Appl. Math.}, owner = {redeker}, pages = {898-939}, title = {Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous Media}, url = {https://academic.oup.com/imamat/article-lookup/doi/10.1093/imamat/hxw023}, volume = {81(5)}, year = 2016 }
  Link
  https://academic.oup.com/imamat/article-lookup/doi/10.1093/imamat/hxw023
7. Dragomirescu, I., Eisenschmidt, K., Rohde, C., & Weigand, B. (2016). Perturbation solutions for the finite radially symmetric Stefan problem. Inter. J. Thermal Sci., 104, 386–395. https://doi.org/10.1016/j.ijthermalsci.2016.01.019
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  BibTeX
  @article{dragomirescu2016perturbation, author = {Dragomirescu, Ioana and Eisenschmidt, Kathrin and Rohde, Christian and Weigand, Bernhard}, doi = {https://doi.org/10.1016/j.ijthermalsci.2016.01.019}, journal = {Inter. J. Thermal Sci.}, owner = {joosde}, pages = {386-395}, title = {Perturbation solutions for the finite radially symmetric Stefan problem}, url = {http://www.sciencedirect.com/science/article/pii/S1290072916000326}, volume = 104, year = 2016 }
  Link
  http://www.sciencedirect.com/science/article/pii/S1290072916000326
8. Köppel, M., & Rohde, C. (2016). Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media. PAMM Proc. Appl. Math. Mech., 16(1), 749–750. https://doi.org/10.1002/pamm.201610363
  - BibTeX
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  BibTeX
  @article{koppel2016uncertainty, author = {K{\"o}ppel, Markus and Rohde, Christian}, doi = {10.1002/pamm.201610363}, journal = {PAMM Proc. Appl. Math. Mech.}, number = 1, owner = {seusdd}, pages = {749–750}, publisher = {WILEY-VCH Verlag}, title = {Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media}, url = {http://onlinelibrary.wiley.com/doi/10.1002/pamm.201610363/abstract}, volume = 16, year = 2016 }
  Link
  http://onlinelibrary.wiley.com/doi/10.1002/pamm.201610363/abstract
9. Dragomirescu, F. I., Eisenschmidt, K., Rohde, C., & Weigand, B. (2016). Perturbation solutions for the finite radially symmetric Stefan problem. INTERNATIONAL JOURNAL OF THERMAL SCIENCES, 104, 386–395. https://doi.org/10.1016/j.ijthermalsci.2016.01.019
  - BibTeX
  BibTeX
  @article{dragomirescu2016perturbation, affiliation = {Dragomirescu, FI (Reprint Author), Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Dragomirescu, Florica Ioana; Rohde, Christian, Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Eisenschmidt, Kathrin; Weigand, Bernhard, Univ Stuttgart, Inst Aerosp Thermodynam, Pfaffenwaldring 31, D-70569 Stuttgart, Germany.}, author = {Dragomirescu, Florica Ioana and Eisenschmidt, Kathrin and Rohde, Christian and Weigand, Bernhard}, doi = {10.1016/j.ijthermalsci.2016.01.019}, eissn = {1778-4166}, issn = {1290-0729}, journal = {INTERNATIONAL JOURNAL OF THERMAL SCIENCES}, language = {English}, month = {06}, pages = {386-395}, publisher = {ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER}, research-areas = {Thermodynamics; Engineering}, title = {Perturbation solutions for the finite radially symmetric Stefan problem}, type = {Article}, unique-id = {ISI:000376696700033}, volume = 104, year = 2016 }
10. Diehl, D., Kremser, J., Kröner, D., & Rohde, C. (2016). Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions. Appl. Math. Comput., 272(2), 309–335. https://doi.org/10.1016/j.amc.2015.09.080
  - BibTeX
  - Link
  BibTeX
  @article{DKKR16, abstract = {Compressible liquid–vapor flow with phase transitions can be described by systems of Navier–Stokes–Korteweg type. They extend the Navier–Stokes equations by nonlinear higher-grade terms which take the form of either differential or nonlocal integral operators. A numerical approximation method on the basis of the Local Discontinuous Galerkin method in multiple space dimensions is suggested for isothermal flows. It relies on a specific discretization of a non-conservative formulation. To enhance the performance of the overall scheme two techniques are used: (i) local spatial adaptivity based on gradient indicators for the density and (ii) parallelism based on domain decomposition. The paper concludes with numerical experiments in two and three space dimensions. They show the reliability and efficiency of the proposed approach as well as they demonstrate the applicability of the models for several important phase transition phenomena.}, author = {Diehl, D. and Kremser, J. and Kr{\"o}ner, D. and Rohde, C.}, doi = {10.1016/j.amc.2015.09.080}, issn = {0096-3003}, journal = {Appl. Math. Comput.}, number = 2, owner = {seusdd}, pages = {309-335}, title = {Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions}, url = {https://doi.org/10.1016/j.amc.2015.09.080}, volume = 272, year = 2016 }
  Link
  https://doi.org/10.1016/j.amc.2015.09.080
11. Diehl, D., Kremser, J., Kröner, D., & Rohde, C. (2016). Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions. Appl. Math. Comput., 272(2), 309–335. https://doi.org/10.1016/j.amc.2015.09.080
  - BibTeX
  - Link
  BibTeX
  @article{DKKR16, abstract = {Compressible liquid–vapor flow with phase transitions can be described by systems of Navier–Stokes–Korteweg type. They extend the Navier–Stokes equations by nonlinear higher-grade terms which take the form of either differential or nonlocal integral operators. A numerical approximation method on the basis of the Local Discontinuous Galerkin method in multiple space dimensions is suggested for isothermal flows. It relies on a specific discretization of a non-conservative formulation. To enhance the performance of the overall scheme two techniques are used: (i) local spatial adaptivity based on gradient indicators for the density and (ii) parallelism based on domain decomposition. The paper concludes with numerical experiments in two and three space dimensions. They show the reliability and efficiency of the proposed approach as well as they demonstrate the applicability of the models for several important phase transition phenomena.}, author = {Diehl, D. and Kremser, J. and Kröner, D. and Rohde, C.}, doi = {10.1016/j.amc.2015.09.080}, issn = {0096-3003}, journal = {Appl. Math. Comput.}, number = 2, owner = {seusdd}, pages = {309-335}, title = {Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions}, url = {https://doi.org/10.1016/j.amc.2015.09.080}, volume = 272, year = 2016 }
  Link
  https://doi.org/10.1016/j.amc.2015.09.080
12. Colombo, R. M., LeFloch, P. G., & Rohde, C. (2016). Hyperbolic techniques in Modelling, Analysis and Numerics. Oberwolfach Reports, 13, 1683–1751. https://doi.org/10.4171/OWR/2016/30
  - BibTeX
  - Link
  BibTeX
  @article{colombo2016hyperbolic, author = {Colombo, R. M. and LeFloch, P. G. and Rohde, C.}, doi = {10.4171/OWR/2016/30}, journal = {Oberwolfach Reports}, note = {Abstracts from the workshop held June 19--25, 2016, Organized by Rinaldo M. Colombo, Philippe G. LeFloch and Christian Rohde}, owner = {szur}, pages = {1683-1751}, title = {Hyperbolic techniques in Modelling, Analysis and Numerics}, url = {http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=13&iss=2&rank=12}, volume = 13, year = 2016 }
  Link
  http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=13&iss=2&rank=12
13. Betancourt, F., & Rohde, C. (2016). Finite-volume schemes for Friedrichs systems with involutions. APPLIED MATHEMATICS AND COMPUTATION, 272(2), 420–439. https://doi.org/10.1016/j.amc.2015.03.050
  - BibTeX
  BibTeX
  @article{betancourt2016finitevolume, affiliation = {Rohde, C (Reprint Author), Univ Stuttgart, Inst Angew Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Betancourt, Fernando, Univ Concepcion, CI2MA, Concepcion, Chile. Betancourt, Fernando, Univ Concepcion, Dept Ingn Met, Concepcion, Chile. Rohde, Christian, Univ Stuttgart, Inst Angew Anal \& Numer Simulat, D-70569 Stuttgart, Germany.}, author = {Betancourt, Fernando and Rohde, Christian}, doi = {10.1016/j.amc.2015.03.050}, eissn = {1873-5649}, issn = {0096-3003}, journal = {APPLIED MATHEMATICS AND COMPUTATION}, language = {English}, month = {01}, number = 2, pages = {420-439}, publisher = {ELSEVIER SCIENCE INC}, research-areas = {Mathematics}, title = {Finite-volume schemes for Friedrichs systems with involutions}, type = {Article}, unique-id = {ISI:000364538800012}, volume = 272, year = 2016 }
2015
1. Rybak, I., Magiera, J., Helmig, R., & Rohde, C. (2015). Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems. Comput. Geosci., 19, 299–309. https://doi.org/10.1007/s10596-015-9469-8
  - BibTeX
  BibTeX
  @article{rybak2015multirate, affiliation = {Rybak, I (Reprint Author), Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Rybak, Iryna; Magiera, Jim; Rohde, Christian, Univ Stuttgart, Inst Appl Anal \& Numer Simulat, D-70569 Stuttgart, Germany. Helmig, Rainer, Univ Stuttgart, Inst Modelling Hydraul \& Environm Syst, D-70569 Stuttgart, Germany.}, author = {Rybak, Iryna and Magiera, Jim and Helmig, Rainer and Rohde, Christian}, doi = {10.1007/s10596-015-9469-8}, eissn = {1573-1499}, issn = {1420-0597}, journal = {Comput. Geosci.}, language = {English}, month = {04}, pages = {299-309}, publisher = {SPRINGER}, research-areas = {Computer Science; Geology}, title = {Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems}, type = {Article}, unique-id = {ISI:000355335100003}, volume = 19, year = 2015 }
2. Rohde, C., & Zeiler, C. (2015). A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension. Appl. Numer. Math., 95, 267--279. https://doi.org/10.1016/j.apnum.2014.05.001
  - BibTeX
  - Link
  BibTeX
  @article{rohde2015relaxation, abstract = {The dynamics of two-phase flows depend crucially on interfacial effects like surface tension and phase transition. A numerical method for compressible inviscid flows is proposed that accounts in particular for these two effects. The approach relies on the solution of Riemann-like problems across the interface that separates the liquid and the vapour phase. Since the analytical solutions of the Riemann problems are only known in particular cases an approximative Riemann solver for arbitrary settings is constructed. The approximative solutions rely on the relaxation technique. The local well-posedness of the approximative solver is proven. Finally we present numerical experiments for radially symmetric configurations that underline the reliability and efficiency of the numerical scheme.}, author = {Rohde, C. and Zeiler, C.}, doi = {10.1016/j.apnum.2014.05.001}, issn = {0168-9274}, journal = {Appl. Numer. Math.}, mrclass = {65M25 (76N99 76T10)}, mrnumber = {3349699}, owner = {seusdd}, pages = {267--279}, title = {A relaxation {R}iemann solver for compressible two-phase flow with phase transition and surface tension}, url = {http://dx.doi.org/10.1016/j.apnum.2014.05.001}, volume = 95, year = 2015 }
  Link
  http://dx.doi.org/10.1016/j.apnum.2014.05.001
3. Kissling, F., & Rohde, C. (2015). The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case. Multiscale Model. Simul., 13 no. 4, 1507–1541. https://doi.org/10.1137/120899236
  - BibTeX
  - Link
  BibTeX
  @article{kissling2015computation, author = {Kissling, F. and Rohde, C.}, doi = {10.1137/120899236}, journal = {Multiscale Model. Simul.}, owner = {seusdd}, pages = {1507-1541}, title = {The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case}, url = {http://epubs.siam.org/doi/abs/10.1137/120899236}, volume = {13 no. 4}, year = 2015 }
  Link
  http://epubs.siam.org/doi/abs/10.1137/120899236
4. Neusser, J., Rohde, C., & Schleper, V. (2015). Relaxation of the Navier-Stokes-Korteweg equations for compressible two-phase flow with phase transition. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 79(12), 615–639. https://doi.org/10.1002/fld.4065
  - BibTeX
  BibTeX
  @article{neusser2015relaxation, affiliation = {Neusser, J (Reprint Author), Univ Stuttgart, Inst Angew Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Neusser, J.; Rohde, C.; Schleper, V., Univ Stuttgart, Inst Angew Anal \& Numer Simulat, D-70569 Stuttgart, Germany.}, author = {Neusser, Jochen and Rohde, Christian and Schleper, Veronika}, doi = {10.1002/fld.4065}, eissn = {1097-0363}, issn = {0271-2091}, journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS}, language = {English}, month = {12}, number = 12, pages = {615-639}, publisher = {WILEY-BLACKWELL}, research-areas = {Computer Science; Mathematics; Mechanics; Physics}, researcherid-numbers = {dashtbozorgi, bahman/F-4393-2011}, title = {Relaxation of the Navier-Stokes-Korteweg equations for compressible two-phase flow with phase transition}, type = {Article}, unique-id = {ISI:000365950100001}, volume = 79, year = 2015 }
5. Neusser, J., Rohde, C., & Schleper, V. (2015). Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase flow with phase transition. J. Numer. Meth. Fluids, 79(12), 615–639. https://doi.org/10.1002/fld.4065
  - BibTeX
  - Link
  BibTeX
  @article{neusser2015relaxed, abstract = {The Navier�Stokes�Korteweg (NSK) system is a classical diffuse-interface model for compressible two-phase flow. However, the direct numerical simulation based on the NSK system is quite expensive and in some cases even not possible. We propose a lower-order relaxation of the NSK system with hyperbolic first-order part. This allows applying numerical methods for hyperbolic conservation laws and removing some of the difficulties of the original NSK system. To illustrate the new ansatz, we first present a local discontinuous Galerkin method in one and two spatial dimensions. It is shown that we can compute initial boundary value problems with realistic density ratios and perform stable computations for small interfacial widths. Second, we show that it is possible to construct a semi-discrete finite-volume scheme that satisfies a discrete entropy inequality.}, author = {Neusser, J. and Rohde, C. and Schleper, V.}, doi = {10.1002/fld.4065}, journal = {J. Numer. Meth. Fluids}, month = {12}, number = 12, owner = {schleper}, pages = {615-639}, title = {Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase flow with phase transition}, url = {http://onlinelibrary.wiley.com/doi/10.1002/fld.4065/full}, volume = 79, year = 2015 }
  Link
  http://onlinelibrary.wiley.com/doi/10.1002/fld.4065/full
6. Kroeker, I., Nowak, W., & Rohde, C. (2015). A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems. COMPUTATIONAL GEOSCIENCES, 19(2), 269–284. https://doi.org/10.1007/s10596-014-9464-5
  - BibTeX
  BibTeX
  @article{kroeker2015stochastically, affiliation = {Kroker, I (Reprint Author), Univ Stuttgart, IANS, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Kroeker, Ilja; Rohde, Christian, Univ Stuttgart, IANS, D-70569 Stuttgart, Germany. Nowak, Wolfgang, Univ Stuttgart, Inst Wasser \& Umweltsystemmodellierung, D-70569 Stuttgart, Germany.}, author = {Kroeker, Ilja and Nowak, Wolfgang and Rohde, Christian}, doi = {10.1007/s10596-014-9464-5}, eissn = {1573-1499}, issn = {1420-0597}, journal = {COMPUTATIONAL GEOSCIENCES}, language = {English}, month = {04}, number = 2, pages = {269-284}, publisher = {SPRINGER}, research-areas = {Computer Science; Geology}, title = {A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems}, type = {Article}, unique-id = {ISI:000355335100001}, volume = 19, year = 2015 }
7. Kröker, I., Nowak, W., & Rohde, C. (2015). A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems. Comput. Geosci., 19(2), 269--284. https://doi.org/10.1007/s10596-014-9464-5
  - BibTeX
  - Link
  BibTeX
  @article{kroker2015stochastically, author = {Kröker, Ilja and Nowak, Wolfgang and Rohde, Christian}, doi = {10.1007/s10596-014-9464-5}, issn = {1420-0597}, journal = {Comput. Geosci.}, language = {English}, number = 2, owner = {seusdd}, pages = {269--284}, publisher = {Springer International Publishing}, title = {A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems}, url = {http://dx.doi.org/10.1007/s10596-014-9464-5}, volume = 19, year = 2015 }
  Link
  http://dx.doi.org/10.1007/s10596-014-9464-5
2014
1. Bürger, R., Kröker, I., & Rohde, C. (2014). A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit. ZAMM Z. Angew. Math. Mech., 94(10), 793–817. https://doi.org/10.1002/zamm.201200174
  - BibTeX
  - Link
  BibTeX
  @article{burger2014hybrid, author = {B{\"u}rger, R. and Kr{\"o}ker, I. and Rohde, C.}, doi = {10.1002/zamm.201200174}, journal = {ZAMM Z. Angew. Math. Mech.}, number = 10, owner = {seusdd}, pages = {793-817}, title = {A hybrid stochastic {G}alerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit}, url = {http://dx.doi.org/10.1002/zamm.201200174}, volume = 94, year = 2014 }
  Link
  http://dx.doi.org/10.1002/zamm.201200174
2. Ehlers, W., Helmig, R., & Rohde, C. (2014). Editorial: Deformation and transport phenomena in porous media. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift F�r Angewandte Mathematik Und Mechanik, 94(7–8), 559--559. https://doi.org/10.1002/zamm.201400559
  - BibTeX
  - Link
  BibTeX
  @article{ehlers2014editorial, author = {Ehlers, Wolfgang and Helmig, Rainer and Rohde, Christian}, doi = {10.1002/zamm.201400559}, issn = {1521-4001}, journal = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f�r Angewandte Mathematik und Mechanik}, number = {7-8}, owner = {seusdd}, pages = {559--559}, publisher = {WILEY-VCH Verlag}, title = {Editorial: Deformation and transport phenomena in porous media}, url = {http://dx.doi.org/10.1002/zamm.201400559}, volume = 94, year = 2014 }
  Link
  http://dx.doi.org/10.1002/zamm.201400559
3. Chalons, C., Engel, P., & Rohde, C. (2014). A Conservative and Convergent Scheme for Undercompressive Shock Waves. SIAM J. Numer. Anal., 52(1), 554–579. http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=732
  - BibTeX
  - Link
  BibTeX
  @article{chalons2014conservative, author = {Chalons, C. and Engel, P. and Rohde, C.}, journal = {SIAM J. Numer. Anal.}, note = {accepted}, number = 1, owner = {ingrid}, pages = {554-579}, title = {A Conservative and Convergent Scheme for Undercompressive Shock Waves}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=732}, volume = 52, year = 2014 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=732
4. Engel, P., Viorel, A., & Rohde, C. (2014). A Low-Order Approximation for Viscous-Capillary Phase Transition Dynamics. Port. Math., 70(4), 319–344. http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=723
  - BibTeX
  - Link
  BibTeX
  @article{engel2014loworder, author = {Engel, P. and Viorel, A. and Rohde, C.}, journal = {Port. Math.}, number = 4, pages = {319-344}, title = {A Low-Order Approximation for Viscous-Capillary Phase Transition Dynamics}, url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=723}, volume = 70, year = 2014 }
  Link
  http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=723
5. Köppel, M., Kröker, I., & Rohde, C. (2014). Stochastic Modeling for Heterogeneous Two-Phase Flow. In J. Fuhrmann, M. Ohlberger, & C. Rohde (Eds.), Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects (Vol. 77, pp. 353–361). Springer International Publishing. https://doi.org/10.1007/978-3-319-05684-5_34
  - BibTeX
  - Link
  BibTeX
  @incollection{koppel2014stochastic, author = {K{\"o}ppel, M. and Kr{\"o}ker, I. and Rohde, C.}, booktitle = {Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects}, doi = {10.1007/978-3-319-05684-5_34}, editor = {Fuhrmann, J{\"u}rgen and Ohlberger, Mario and Rohde, Christian}, isbn = {978-3-319-05683-8}, language = {English}, owner = {seusdd}, pages = {353-361}, publisher = {Springer International Publishing}, series = {Springer Proceedings in Mathematics \& Statistics}, title = {Stochastic Modeling for Heterogeneous Two-Phase Flow}, url = {http://dx.doi.org/10.1007/978-3-319-05684-5_34}, volume = 77, year = 2014 }
  Link
  http://dx.doi.org/10.1007/978-3-319-05684-5_34
6. Fechter, S., Zeiler, C., Munz, C.-D., & Rohde, C. (2014). Simulation of compressible multi-phase flows at extreme ambient conditions using a Discontinuous-Galerkin method. ILASS Europe, 26th European Conference on Liquid Atomization and Spray Systems.
  - BibTeX
  BibTeX
  @inproceedings{fechter2014simulation, author = {Fechter, Stefan and Zeiler, Christoph and Munz, Claus-Dieter and Rohde, Christian}, booktitle = {ILASS Europe, 26th European Conference on Liquid Atomization and Spray Systems}, owner = {seusdd}, title = {Simulation of compressible multi-phase flows at extreme ambient conditions using a Discontinuous-Galerkin method}, year = 2014 }
7. Kabil, B., & Rohde, C. (2014). The influence of surface tension and configurational forces on the stability of liquid-vapor interfaces. Nonlinear Analysis: Theory, Methods & Applications, 107(0), 63–75. http://dx.doi.org/10.1016/j.na.2014.04.003
  - BibTeX
  - Link
  BibTeX
  @article{kabil2014influence, abstract = {Abstract The stability of liquid�vapor interfaces in a multidimensional van der Waals fluid is analyzed. We consider interfaces which connect liquid and vapor states as subsonic shock waves. Surface tension and configurational forces in the form of a kinetic relation determine the evolution of the interface. Stability results for the interface in the sense of energy estimates for solutions of the linearized problem are given. The normal mode analysis of the problem shows that in particular the uniform Kreiss�Lopatinskii condition is satisfied as long as surface tension and amount of energy dissipation are positive but remain small. The analysis relies on Benzoni-Gavage and Freist�hler (2004), where surface tension is arbitrary but energy dissipation is zero. Non-stability results for the same system without surface tension and without energy dissipation can be found in Benzoni-Gavage (1999).}, author = {Kabil, Bugra and Rohde, Christian}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, number = 0, owner = {kabil}, pages = {63 - 75}, title = {The influence of surface tension and configurational forces on the stability of liquid-vapor interfaces}, type = {Article}, url = {http://dx.doi.org/10.1016/j.na.2014.04.003}, volume = 107, year = 2014 }
  Link
  http://dx.doi.org/10.1016/j.na.2014.04.003
8. Armiti-Juber, A., & Rohde, C. (2014). Almost Parallel Flows in Porous Media. In J. Fuhrmann, M. Ohlberger, & C. Rohde (Eds.), Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems (Vol. 78, pp. 873–881). Springer International Publishing. https://doi.org/10.1007/978-3-319-05591-6_88
  - BibTeX
  - Link
  BibTeX
  @incollection{armitijuber2014almost, author = {Armiti-Juber, A. and Rohde, C.}, booktitle = {Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems}, doi = {10.1007/978-3-319-05591-6_88}, editor = {Fuhrmann, J�rgen and Ohlberger, Mario and Rohde, Christian}, owner = {seusdd}, pages = {873-881}, publisher = {Springer International Publishing}, title = {Almost Parallel Flows in Porous Media}, url = {http://dx.doi.org/10.1007/978-3-319-05591-6_88}, volume = 78, year = 2014 }
  Link
  http://dx.doi.org/10.1007/978-3-319-05591-6_88
9. Corli, A., Rohde, C., & Schleper, V. (2014). Parabolic approximations of diffusive-dispersive equations. J. Math. Anal. Appl., 414, 773–798. http://dx.doi.org/10.1016/j.jmaa.2014.01.049
  - BibTeX
  - Link
  BibTeX
  @article{corli2014parabolic, author = {Corli, A. and Rohde, C. and Schleper, V.}, journal = {J. Math. Anal. Appl.}, owner = {schleper}, pages = {773-798}, title = {Parabolic approximations of diffusive-dispersive equations.}, url = {http://dx.doi.org/10.1016/j.jmaa.2014.01.049}, volume = 414, year = 2014 }
  Link
  http://dx.doi.org/10.1016/j.jmaa.2014.01.049
2013
1. Eck, Ch., Kutter, M., Sändig, A.-M., & Rohde, Ch. (2013). A two scale model for liquid phase epitaxy with elasticity: An iterative procedure. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik, 93(10–11), 745--761. https://doi.org/10.1002/zamm.201200238
  - BibTeX
  - Link
  BibTeX
  @article{eck2013scale, author = {Eck, Ch. and Kutter, M. and S{\"a}ndig, A.-M. and Rohde, Ch.}, doi = {10.1002/zamm.201200238}, issn = {1521-4001}, journal = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}, number = {10-11}, pages = {745--761}, publisher = {WILEY-VCH Verlag}, title = {A two scale model for liquid phase epitaxy with elasticity: An iterative procedure}, url = {http://dx.doi.org/10.1002/zamm.201200238}, volume = 93, year = 2013 }
  Link
  http://dx.doi.org/10.1002/zamm.201200238
2. Eisenschmidt, K., Rauschenberger, P., Rohde, C., & Weigand, B. (2013). Modelling of freezing processes in super-cooled droplets on sub-grid scale. ILASS�Europe, 25th European Conference on Liquid Atomization and Spray Systems.
  - BibTeX
  BibTeX
  @inproceedings{eisenschmidt2013modelling, author = {Eisenschmidt, K. and Rauschenberger, P. and Rohde, C. and Weigand, B.}, booktitle = {ILASS�Europe, 25th European Conference on Liquid Atomization and Spray Systems}, title = {Modelling of freezing processes in super-cooled droplets on sub-grid scale}, year = 2013 }
3. Rohde, C., Wang, W., & Xie, F. (2013). Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation Hydrodynamics Model. Mathematical Models and Methods in Applied Sciences, 23(03), 441--469. https://doi.org/10.1142/S0218202512500522
  - BibTeX
  - Link
  BibTeX
  @article{rohde2013decay, author = {Rohde, Christian and Wang, Wenjun and Xie, Feng}, doi = {10.1142/S0218202512500522}, eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218202512500522}, journal = {Mathematical Models and Methods in Applied Sciences}, number = 03, pages = {441--469}, title = {Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation Hydrodynamics Model}, url = {http://www.worldscientific.com/doi/abs/10.1142/S0218202512500522}, volume = 23, year = 2013 }
  Link
  http://www.worldscientific.com/doi/abs/10.1142/S0218202512500522
4. Rohde, C., Wang, W., & Xie, F. (2013). Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves. Communications on Pure and Applied Analysis, 12(5), 2145--2171. https://doi.org/10.3934/cpaa.2013.12.2145
  - BibTeX
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  BibTeX
  @article{rohde2013hyperbolichyperbolic, author = {Rohde, Christian and Wang, Wenjun and Xie, Feng}, doi = {10.3934/cpaa.2013.12.2145}, journal = {Communications on Pure and Applied Analysis}, number = 5, pages = {2145--2171}, title = {Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves}, url = {http://dx.doi.org/10.3934/cpaa.2013.12.2145}, volume = 12, year = 2013 }
  Link
  http://dx.doi.org/10.3934/cpaa.2013.12.2145
2012
1. Corli, A., & Rohde, C. (2012). Singular limits for a parabolic-elliptic regularization of scalar conservation laws. J. Differential Equations, 253(5), 1399--1421. https://doi.org/10.1016/j.jde.2012.05.006
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  BibTeX
  @article{corli2012singular, author = {Corli, Andrea and Rohde, Christian}, coden = {JDEQAK}, doi = {10.1016/j.jde.2012.05.006}, fjournal = {Journal of Differential Equations}, issn = {0022-0396}, journal = {J. Differential Equations}, mrclass = {35L65 (35C07 35L67)}, mrnumber = {2927386}, number = 5, owner = {szur}, pages = {1399--1421}, title = {Singular limits for a parabolic-elliptic regularization of scalar conservation laws}, url = {http://dx.doi.org/10.1016/j.jde.2012.05.006}, volume = 253, year = 2012 }
  Link
  http://dx.doi.org/10.1016/j.jde.2012.05.006
2. Dreyer, W., Giesselmann, J., Kraus, C., & Rohde, C. (2012). Asymptotic Analysis for Korteweg Models. Interfaces Free Bound., 14, 105–143. http://www.ems-ph.org/journals/show_pdf.php?issn=1463-9963&vol=14&iss=1&rank=4
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  BibTeX
  @article{dreyer2012asymptotic, author = {Dreyer, Wolfgang and Giesselmann, Jan and Kraus, Christiane and Rohde, Christian}, journal = {Interfaces Free Bound.}, owner = {Jan}, pages = {105 - 143}, title = {Asymptotic Analysis for Korteweg Models}, url = {http://www.ems-ph.org/journals/show_pdf.php?issn=1463-9963&vol=14&iss=1&rank=4}, volume = 14, year = 2012 }
  Link
  http://www.ems-ph.org/journals/show_pdf.php?issn=1463-9963&vol=14&iss=1&rank=4
3. Engel, P., & Rohde, C. (2012). On the Space-Time Expansion Discontinuous Galerkin Method. In T. Li & S. Jiang (Eds.), Hyperbolic Problems: Theory, Numerics and Applications (pp. 406--414).
  - BibTeX
  BibTeX
  @inproceedings{engel2012spacetime, author = {Engel, Patrick and Rohde, Christian}, booktitle = {Hyperbolic Problems: Theory, Numerics and Applications}, editor = {Li, T. and Jiang, S.}, pages = {406--414}, series = {Series in Contemporary Applied Mathematics}, title = {On the Space-Time Expansion Discontinuous Galerkin Method}, year = 2012 }
4. Jaegle, F., Rohde, C., & Zeiler, C. (2012). A multiscale method for compressible liquid-vapor flow with surface tension. ESAIM: Proc., 38, 387–408. https://doi.org/10.1051/proc/201238022
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  BibTeX
  @article{jaegle2012multiscale, abstract = {Discontinuous Galerkin methods have become a powerful tool for approximation the solution of compressible ?ow problems. Their direct use for two-phase ?ow problems with phase transformation is not straightforward because this type of ?ows requires a detailed tracking of the phase front. We consider the fronts in this contribution as sharp interfaces and propose a novel multiscale approach. It combines an e?cient high-order Discontinuous Galerkin solver for the computation in the bulk phases on the macro-scale with the use of a generalized Riemann solver on the micro-scale. The Riemann solver takes into account the e?ects of moderate surface tension via the curvature of the sharp interface as well as phase transformation. First numerical experiments in three space dimensions underline the overall performance of the method.}, author = {Jaegle, Felix and Rohde, Christian and Zeiler, Christoph}, doi = {10.1051/proc/201238022}, journal = {ESAIM: Proc.}, owner = {seusdd}, pages = {387-408}, title = {A multiscale method for compressible liquid-vapor flow with surface tension}, url = {http://dx.doi.org/10.1051/proc/201238022}, volume = 38, year = 2012 }
  Link
  http://dx.doi.org/10.1051/proc/201238022
5. Kissling, F., & Rohde, C. (2012). Numerical Simulation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method. In T. Li & S. Jiang (Eds.), Hyperbolic Problems: Theory, Numerics and Applications (pp. 469--478).
  - BibTeX
  BibTeX
  @conference{kissling2012numerical, author = {Kissling, F. and Rohde, C.}, booktitle = {Hyperbolic Problems: Theory, Numerics and Applications}, editor = {Li, T. and Jiang, S.}, owner = {kissling}, pages = {469--478}, series = {Series in Contemporary Applied Mathematics}, title = {Numerical {S}imulation of {N}onclassical {S}hock {W}aves in {P}orous {M}edia with a {H}eterogeneous {M}ultiscale {M}ethod}, year = 2012 }
6. Richter, T., Rudlof, S., Adjibadji, B., Bernlöhr, H., Gröninger, C., Munz, C.-D., Stock, A., Rohde, C., & Helmig, R. (2012). ViPLab: a virtual programming laboratory for mathematics and engineering. Interactive Technology and Smart Education, 9, 246–262. https://doi.org/10.1108/17415651211284039
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  BibTeX
  @article{richter2012viplab, author = {Richter, Thomas and Rudlof, Stephan and Adjibadji, B. and Bernlöhr, Heiko and Gröninger, Christoph and Munz, Claus-Dieter and Stock, Andreas and Rohde, Christian and Helmig, Rainer}, doi = {10.1108/17415651211284039}, journal = {Interactive Technology and Smart Education}, pages = {246 - 262}, title = {ViPLab: a virtual programming laboratory for mathematics and engineering}, volume = 9, year = 2012 }
7. Kröker, I., & Rohde, C. (2012). Finite volume schemes for hyperbolic balance laws with multiplicative noise. Appl. Numer. Math., 62(4), 441--456. https://doi.org/10.1016/j.apnum.2011.01.011
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  BibTeX
  @article{kroker2012finite, author = {Kr{\"o}ker, I. and Rohde, C.}, coden = {ANMAEL}, doi = {10.1016/j.apnum.2011.01.011}, fjournal = {Applied Numerical Mathematics. An IMACS Journal}, issn = {0168-9274}, journal = {Appl. Numer. Math.}, mrclass = {65M08}, mrnumber = {2899255}, number = 4, owner = {szur}, pages = {441--456}, title = {Finite volume schemes for hyperbolic balance laws with multiplicative noise}, url = {http://dx.doi.org/10.1016/j.apnum.2011.01.011}, volume = 62, year = 2012 }
  Link
  http://dx.doi.org/10.1016/j.apnum.2011.01.011
8. Rohde, C., & Xie, F. (2012). Global existence and blowup phenomenon for a 1D radiation hydrodynamics model problem. Math. Methods Appl. Sci., 35(5), 564--573. https://doi.org/10.1002/mma.1593
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  BibTeX
  @article{rohde2012global, author = {Rohde, Christian and Xie, Feng}, doi = {10.1002/mma.1593}, fjournal = {Mathematical Methods in the Applied Sciences}, issn = {0170-4214}, journal = {Math. Methods Appl. Sci.}, mrclass = {35Q35 (35A09 35B44 76X05)}, mrnumber = {2908767}, number = 5, owner = {szur}, pages = {564--573}, title = {Global existence and blowup phenomenon for a 1{D} radiation hydrodynamics model problem}, url = {http://dx.doi.org/10.1002/mma.1593}, volume = 35, year = 2012 }
  Link
  http://dx.doi.org/10.1002/mma.1593
9. Chalons, C., Coquel, F., Engel, P., & Rohde, C. (2012). Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems. SIAM Journal on Scientific Computing, 34(3), A1753--A1776. https://doi.org/10.1137/110848815
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  BibTeX
  @article{chalons2012relaxation, author = {Chalons, C. and Coquel, F. and Engel, P. and Rohde, C.}, doi = {10.1137/110848815}, eprint = {http://epubs.siam.org/doi/pdf/10.1137/110848815}, journal = {SIAM Journal on Scientific Computing}, number = 3, pages = {A1753--A1776}, title = {Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems}, url = {http://epubs.siam.org/doi/abs/10.1137/110848815}, volume = 34, year = 2012 }
  Link
  http://epubs.siam.org/doi/abs/10.1137/110848815
10. Kissling, F., Helmig, R., & Rohde, C. (2012). Simulation of Infiltration Processes in the Unsaturated Zone Using a Multi-Scale Approach. Vadose Zone J., 11(3). https://doi.org/10.2136/vzj2011.0193
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  BibTeX
  @article{kissling2012simulation, author = {Kissling, F. and Helmig, R. and Rohde, C.}, doi = {10.2136/vzj2011.0193}, journal = {Vadose Zone J.}, number = 3, owner = {kissling}, pages = {-}, title = {{S}imulation of {I}nfiltration {P}rocesses in the {U}nsaturated {Z}one {U}sing a {M}ulti-{S}cale {A}pproach}, url = {http://dx.doi.org/10.2136/vzj2011.0193}, volume = 11, year = 2012 }
  Link
  http://dx.doi.org/10.2136/vzj2011.0193
2011
1. Bürger, R., Kröker, I., & Rohde, C. (2011). Uncertainty quantification for a clarifier-thickener model with random feed. In Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2 (Vol. 4, pp. 195--203). Springer. https://doi.org/10.1007/978-3-642-20671-9_21
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  BibTeX
  @incollection{burger2011uncertainty, author = {Bürger, Raimund and Kröker, Ilja and Rohde, Christian}, booktitle = {Finite volumes for complex applications. VI. Problems \& perspectives. Volume 1, 2}, doi = {10.1007/978-3-642-20671-9_21}, owner = {seusdd}, pages = {195--203}, publisher = {Springer}, title = {Uncertainty quantification for a clarifier-thickener model with random feed}, url = {http://dx.doi.org/10.1007/978-3-642-20671-9_21}, volume = 4, year = 2011 }
  Link
  http://dx.doi.org/10.1007/978-3-642-20671-9_21
2. Richter, Th., Rudlof, S., Adjibadji, B., Berlohr, H., Gruninger, Ch., Munz, C.-D., Rohde, Ch., & Helmig, R. (2011). ViPLab - A Virtual Programming Laboratory for Mathematics and Engineering. Proceedings of the 2011 IEEE International Symposium on Multimedia, 537--542. https://doi.org/10.1109/ISM.2011.95
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  BibTeX
  @inproceedings{richter2011viplab, acmid = {2120544}, address = {Washington, DC, USA}, author = {Richter, Th. and Rudlof, S. and Adjibadji, B. and Berlohr, H. and Gruninger, Ch. and Munz, C.-D. and Rohde, Ch. and Helmig, R.}, booktitle = {Proceedings of the 2011 IEEE International Symposium on Multimedia}, doi = {10.1109/ISM.2011.95}, isbn = {978-0-7695-4589-9}, numpages = {6}, pages = {537--542}, publisher = {IEEE Computer Society}, series = {ISM '11}, title = {ViPLab - A Virtual Programming Laboratory for Mathematics and Engineering}, url = {http://dx.doi.org/10.1109/ISM.2011.95}, year = 2011 }
  Link
  http://dx.doi.org/10.1109/ISM.2011.95
2010
1. Kissling, F., & Rohde, C. (2010). The Computation of Nonclassical Shock Waves with a Heterogeneous Multiscale Method. Netw. Heterog. Media, 5(3), 661--674. https://doi.org/10.3934/nhm.2010.5.661
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  @article{kissling2010computation, author = {Kissling, Frederike and Rohde, Christian}, doi = {10.3934/nhm.2010.5.661}, fjournal = {Networks and Heterogeneous Media}, issn = {1556-1801}, journal = {Netw. Heterog. Media}, mrclass = {65M50 (35L65 65M99 76L05 76N15 76S05)}, mrnumber = {2670661 (2011j:65204)}, mrreviewer = {Long An Ying}, number = 3, pages = {661--674}, title = {The {C}omputation of {N}onclassical {S}hock {W}aves with a {H}eterogeneous {M}ultiscale {M}ethod}, url = {http://dx.doi.org/10.3934/nhm.2010.5.661}, volume = 5, year = 2010 }
  Link
  http://dx.doi.org/10.3934/nhm.2010.5.661
2. Rohde, C. (2010). A local and low-order Navier-Stokes-Korteweg system. In Nonlinear partial differential equations and hyperbolic wave phenomena (Vol. 526, pp. 315--337). Amer. Math. Soc. https://doi.org/10.1090/conm/526/10387
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  BibTeX
  @incollection{rohde2010local, address = {Providence, RI}, author = {Rohde, Christian}, booktitle = {Nonlinear partial differential equations and hyperbolic wave phenomena}, doi = {10.1090/conm/526/10387}, mrclass = {35Q30 (35Q53 76N10)}, mrnumber = {2731998 (2012c:35331)}, mrreviewer = {Rapha{\"e}l Danchin}, owner = {szur}, pages = {315--337}, publisher = {Amer. Math. Soc.}, series = {Contemp. Math.}, title = {A local and low-order {N}avier-{S}tokes-{K}orteweg system}, url = {http://dx.doi.org/10.1090/conm/526/10387}, volume = 526, year = 2010 }
  Link
  http://dx.doi.org/10.1090/conm/526/10387
2009
1. Kissling, F., LeFloch, P. G., & Rohde, C. (2009). A Kinetic Decomposition for Singular Limits of non-local Conservation Laws. J. Differential Equations, 247(12), 3338--3356. https://doi.org/10.1016/j.jde.2009.05.006
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  BibTeX
  @article{kissling2009kinetic, author = {Kissling, Frederike and LeFloch, Philippe G. and Rohde, Christian}, coden = {JDEQAK}, doi = {10.1016/j.jde.2009.05.006}, fjournal = {Journal of Differential Equations}, issn = {0022-0396}, journal = {J. Differential Equations}, mrclass = {35L65}, mrnumber = {2571580 (2011a:35334)}, mrreviewer = {Konstantina Trivisa}, number = 12, owner = {szur}, pages = {3338--3356}, title = {{A} {K}inetic {D}ecomposition for {S}ingular {L}imits of non-local {C}onservation {L}aws}, url = {http://dx.doi.org/10.1016/j.jde.2009.05.006}, volume = 247, year = 2009 }
  Link
  http://dx.doi.org/10.1016/j.jde.2009.05.006
2008
1. Rohde, C., Tiemann, N., & Yong, W.-A. (2008). Weak and classical solutions for a model problem in radiation hydrodynamics. In Hyperbolic problems: theory, numerics, applications (pp. 891--899). Springer. https://doi.org/10.1007/978-3-540-75712-2_93
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  BibTeX
  @incollection{rohde2008classical, address = {Berlin}, author = {Rohde, C. and Tiemann, N. and Yong, W.-A.}, booktitle = {Hyperbolic problems: theory, numerics, applications}, doi = {10.1007/978-3-540-75712-2_93}, mrclass = {76W05 (35A01 35D30 35Q35)}, mrnumber = {2549228}, owner = {szur}, pages = {891--899}, publisher = {Springer}, title = {Weak and classical solutions for a model problem in radiation hydrodynamics}, url = {http://dx.doi.org/10.1007/978-3-540-75712-2_93}, year = 2008 }
  Link
  http://dx.doi.org/10.1007/978-3-540-75712-2_93
2. Rohde, C., & Yong, W.-A. (2008). Dissipative entropy and global smooth solutions in radiation hydrodynamics and magnetohydrodynamics. Math. Models Methods Appl. Sci., 18(12), 2151--2174. https://doi.org/10.1142/S0218202508003327
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  @article{rohde2008dissipative, author = {Rohde, Christian and Yong, Wen-An}, doi = {10.1142/S0218202508003327}, fjournal = {Mathematical Models \& Methods in Applied Sciences}, issn = {0218-2025}, journal = {Math. Models Methods Appl. Sci.}, mrclass = {76W05 (35Q35)}, mrnumber = {2477720 (2010a:76094)}, mrreviewer = {Omar Maj}, number = 12, owner = {szur}, pages = {2151--2174}, title = {Dissipative entropy and global smooth solutions in radiation hydrodynamics and magnetohydrodynamics}, url = {http://dx.doi.org/10.1142/S0218202508003327}, volume = 18, year = 2008 }
  Link
  http://dx.doi.org/10.1142/S0218202508003327
3. Dressel, A., & Rohde, C. (2008). A finite-volume approach to liquid-vapour fluids with phase transition. In Finite volumes for complex applications V (pp. 53--68). ISTE, London.
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  BibTeX
  @incollection{dressel2008finitevolume, author = {Dressel, Alexander and Rohde, Christian}, booktitle = {Finite volumes for complex applications {V}}, mrclass = {76M12 (65M06 76T10 80A22)}, mrnumber = {2441446 (2009j:76163)}, mrreviewer = {Jakub Siemek}, owner = {szur}, pages = {53--68}, publisher = {ISTE, London}, title = {A finite-volume approach to liquid-vapour fluids with phase transition}, year = 2008 }
4. Haink, J., & Rohde, C. (2008). Local discontinuous-Galerkin schemes for model problems in phase transition theory. Commun. Comput. Phys., 4, 860–893. https://www.researchgate.net/profile/Christian_Rohde2/publication/228406932_Local_discontinuous-Galerkin_schemes_for_model_problems_in_phase_transition_theory/links/00b4952cb030e0da90000000.pdf
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  BibTeX
  @article{haink2008local, author = {Haink, J. and Rohde, C.}, journal = {Commun. Comput. Phys.}, owner = {joosde}, pages = {860-893}, title = {Local discontinuous-{G}alerkin schemes for model problems in phase transition theory}, url = {https://www.researchgate.net/profile/Christian_Rohde2/publication/228406932_Local_discontinuous-Galerkin_schemes_for_model_problems_in_phase_transition_theory/links/00b4952cb030e0da90000000.pdf}, volume = 4, year = 2008 }
  Link
  https://www.researchgate.net/profile/Christian_Rohde2/publication/228406932_Local_discontinuous-Galerkin_schemes_for_model_problems_in_phase_transition_theory/links/00b4952cb030e0da90000000.pdf
5. Dressel, A., & Rohde, C. (2008). Global existence and uniqueness of solutions for a viscoelastic two-phase model. Indiana Univ. Math. J., 57(2), 717--755. https://doi.org/10.1512/iumj.2008.57.3271
  - BibTeX
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  BibTeX
  @article{dressel2008global, author = {Dressel, Alexander and Rohde, Christian}, coden = {IUMJAB}, doi = {10.1512/iumj.2008.57.3271}, fjournal = {Indiana University Mathematics Journal}, issn = {0022-2518}, journal = {Indiana Univ. Math. J.}, mrclass = {35Q72 (35B30 35D05 74A30 74D10 74H20)}, mrnumber = {2414333 (2009e:35278)}, mrreviewer = {Marcelo M. Cavalcanti}, number = 2, owner = {szur}, pages = {717--755}, title = {Global existence and uniqueness of solutions for a viscoelastic two-phase model}, url = {http://dx.doi.org/10.1512/iumj.2008.57.3271}, volume = 57, year = 2008 }
  Link
  http://dx.doi.org/10.1512/iumj.2008.57.3271
2007
1. Rohde, C., & Yong, W.-A. (2007). The nonrelativistic limit in radiation hydrodynamics. I. Weak entropy solutions for a model problem. J. Differential Equations, 234(1), 91--109. https://doi.org/10.1016/j.jde.2006.11.010
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  @article{rohde2007nonrelativistic, author = {Rohde, Christian and Yong, Wen-An}, coden = {JDEQAK}, doi = {10.1016/j.jde.2006.11.010}, fjournal = {Journal of Differential Equations}, issn = {0022-0396}, journal = {J. Differential Equations}, mrclass = {35Q35}, mrnumber = {2298966 (2008c:35256)}, mrreviewer = {Philippe G. LeFloch}, number = 1, owner = {szur}, pages = {91--109}, title = {The nonrelativistic limit in radiation hydrodynamics. {I}. {W}eak entropy solutions for a model problem}, url = {http://dx.doi.org/10.1016/j.jde.2006.11.010}, volume = 234, year = 2007 }
  Link
  http://dx.doi.org/10.1016/j.jde.2006.11.010
2. Merkle, C., & Rohde, C. (2007). The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques. M2AN Math. Model. Numer. Anal., 41(6), 1089--1123. https://doi.org/10.1051/m2an:2007048
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  BibTeX
  @article{merkle2007sharpinterface, author = {Merkle, Christian and Rohde, Christian}, doi = {10.1051/m2an:2007048}, fjournal = {M2AN. Mathematical Modelling and Numerical Analysis}, issn = {0764-583X}, journal = {M2AN Math. Model. Numer. Anal.}, mrclass = {76T10 (35L65 35Q35 76M25 80A22)}, mrnumber = {2377108 (2008j:76068)}, mrreviewer = {Denis Serre}, number = 6, owner = {szur}, pages = {1089--1123}, title = {The sharp-interface approach for fluids with phase change: {R}iemann problems and ghost fluid techniques}, url = {http://dx.doi.org/10.1051/m2an:2007048}, volume = 41, year = 2007 }
  Link
  http://dx.doi.org/10.1051/m2an:2007048
2006
1. Haink, J., & Rohde, C. (2006). Phase transition in compressible media and nonlocal capillarity terms. In Hyperbolic problems: theory, numerics and applications. I (pp. 147--154). Yokohama Publ., Yokohama.
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  BibTeX
  @incollection{haink2006phase, author = {Haink, Jenny and Rohde, Christian}, booktitle = {Hyperbolic problems: theory, numerics and applications. {I}}, mrclass = {35Q35 (35C07 76D45)}, mrnumber = {2667232}, owner = {szur}, pages = {147--154}, publisher = {Yokohama Publ., Yokohama}, title = {Phase transition in compressible media and nonlocal capillarity terms}, year = 2006 }
2. Diehl, D., & Rohde, C. (2006). On the structure of MHD shock waves in diffusive-dispersive media. J. Math. Fluid Mech., 8(1), 120--145. https://doi.org/10.1007/s00021-004-0149-z
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  BibTeX
  @article{diehl2006structure, author = {Diehl, Dennis and Rohde, Christian}, doi = {10.1007/s00021-004-0149-z}, fjournal = {Journal of Mathematical Fluid Mechanics}, issn = {1422-6928}, journal = {J. Math. Fluid Mech.}, mrclass = {76W05 (35L70 37M20 37N10 76L05)}, mrnumber = {2205154 (2006j:76164)}, mrreviewer = {Dehua Wang}, number = 1, owner = {szur}, pages = {120--145}, title = {On the structure of {MHD} shock waves in diffusive-dispersive media}, url = {http://dx.doi.org/10.1007/s00021-004-0149-z}, volume = 8, year = 2006 }
  Link
  http://dx.doi.org/10.1007/s00021-004-0149-z
3. Merkle, C., & Rohde, C. (2006). Computation of dynamical phase transitions in solids. Appl. Numer. Math., 56(10–11), 1450--1463. https://doi.org/10.1016/j.apnum.2006.03.025
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  BibTeX
  @article{merkle2006computation, author = {Merkle, C. and Rohde, C.}, coden = {ANMAEL}, doi = {10.1016/j.apnum.2006.03.025}, fjournal = {Applied Numerical Mathematics. An IMACS Journal}, issn = {0168-9274}, journal = {Appl. Numer. Math.}, mrclass = {74N99 (74H15 74J40 74N15 82C26)}, mrnumber = {2245467 (2007i:74093)}, number = {10-11}, owner = {szur}, pages = {1450--1463}, title = {Computation of dynamical phase transitions in solids}, url = {http://dx.doi.org/10.1016/j.apnum.2006.03.025}, volume = 56, year = 2006 }
  Link
  http://dx.doi.org/10.1016/j.apnum.2006.03.025
4. Jovanović, V., & Rohde, C. (2006). Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws. SIAM J. Numer. Anal., 43(6), 2423--2449 (electronic). https://doi.org/10.1137/S0036142903438136
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  @article{jovanovic2006error, author = {Jovanovi{\'c}, Vladimir and Rohde, Christian}, doi = {10.1137/S0036142903438136}, fjournal = {SIAM Journal on Numerical Analysis}, issn = {0036-1429}, journal = {SIAM J. Numer. Anal.}, mrclass = {65M12 (35L60 35L65 65M06)}, mrnumber = {2206442 (2006j:65263)}, mrreviewer = {Doron Levy}, number = 6, owner = {szur}, pages = {2423--2449 (electronic)}, title = {Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws}, url = {http://dx.doi.org/10.1137/S0036142903438136}, volume = 43, year = 2006 }
  Link
  http://dx.doi.org/10.1137/S0036142903438136
2005
1. Rohde, C. (2005). Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms. SIAM J. Math. Anal., 37(1), 103--129 (electronic). https://doi.org/10.1137/S0036141004443300
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  @article{rohde2005scalar, author = {Rohde, Christian}, doi = {10.1137/S0036141004443300}, fjournal = {SIAM Journal on Mathematical Analysis}, issn = {0036-1410}, journal = {SIAM J. Math. Anal.}, mrclass = {35L65 (35L67)}, mrnumber = {2176925 (2006k:35183)}, mrreviewer = {Stefano Bianchini}, number = 1, owner = {szur}, pages = {103--129 (electronic)}, title = {Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms}, url = {http://dx.doi.org/10.1137/S0036141004443300}, volume = 37, year = 2005 }
  Link
  http://dx.doi.org/10.1137/S0036141004443300
2. Coquel, F., Diehl, D., Merkle, C., & Rohde, C. (2005). Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows. In Numerical methods for hyperbolic and kinetic problems (Vol. 7, pp. 239--270). Eur. Math. Soc., Zürich. https://doi.org/10.4171/012-1/11
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  BibTeX
  @incollection{coquel2005sharp, author = {Coquel, F. and Diehl, D. and Merkle, C. and Rohde, C.}, booktitle = {Numerical methods for hyperbolic and kinetic problems}, doi = {10.4171/012-1/11}, mrclass = {80A22 (65M06 76N99)}, mrnumber = {2186374 (2006j:80005)}, mrreviewer = {Ulisse Stefanelli}, owner = {szur}, pages = {239--270}, publisher = {Eur. Math. Soc., Z\"urich}, series = {IRMA Lect. Math. Theor. Phys.}, title = {Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows}, url = {http://dx.doi.org/10.4171/012-1/11}, volume = 7, year = 2005 }
  Link
  http://dx.doi.org/10.4171/012-1/11
3. Gander, M. J., & Rohde, C. (2005). Overlapping Schwarz waveform relaxation for convection-dominated nonlinear conservation laws. SIAM J. Sci. Comput., 27(2), 415--439. https://doi.org/10.1137/030601090
  - BibTeX
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  BibTeX
  @article{gander2005overlapping, author = {Gander, Martin J. and Rohde, Christian}, doi = {10.1137/030601090}, fjournal = {SIAM Journal on Scientific Computing}, issn = {1064-8275}, journal = {SIAM J. Sci. Comput.}, mrclass = {35L65 (35B25 35K55 65M55)}, mrnumber = {2202227 (2006i:35234)}, number = 2, owner = {szur}, pages = {415--439}, title = {Overlapping {S}chwarz waveform relaxation for convection-dominated nonlinear conservation laws}, url = {http://dx.doi.org/10.1137/030601090}, volume = 27, year = 2005 }
  Link
  http://dx.doi.org/10.1137/030601090
4. Jovanović, V., & Rohde, C. (2005). Finite-volume schemes for Friedrichs systems in multiple space dimensions: a priori and a posteriori error estimates. Numer. Methods Partial Differential Equations, 21(1), 104--131. https://doi.org/10.1002/num.20026
  - BibTeX
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  BibTeX
  @article{jovanovic2005finitevolume, author = {Jovanovi{\'c}, Vladimir and Rohde, Christian}, doi = {10.1002/num.20026}, fjournal = {Numerical Methods for Partial Differential Equations. An International Journal}, issn = {0749-159X}, journal = {Numer. Methods Partial Differential Equations}, mrclass = {65M06 (35L45 65M15)}, mrnumber = {2100303 (2005h:65134)}, number = 1, owner = {szur}, pages = {104--131}, title = {Finite-volume schemes for {F}riedrichs systems in multiple space dimensions: a priori and a posteriori error estimates}, url = {http://dx.doi.org/10.1002/num.20026}, volume = 21, year = 2005 }
  Link
  http://dx.doi.org/10.1002/num.20026
5. Rohde, C. (2005). On local and non-local Navier-Stokes-Korteweg systems for liquid-vapour phase transitions. ZAMM Z. Angew. Math. Mech., 85(12), 839--857. https://doi.org/10.1002/zamm.200410211
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  @article{rohde2005local, author = {Rohde, Christian}, doi = {10.1002/zamm.200410211}, fjournal = {ZAMM. Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics}, issn = {0044-2267}, journal = {ZAMM Z. Angew. Math. Mech.}, mrclass = {35Q35 (35B30 76N10 76T10 80A22)}, mrnumber = {2184845 (2006h:35217)}, number = 12, owner = {szur}, pages = {839--857}, title = {On local and non-local {N}avier-{S}tokes-{K}orteweg systems for liquid-vapour phase transitions}, url = {http://dx.doi.org/10.1002/zamm.200410211}, volume = 85, year = 2005 }
  Link
  http://dx.doi.org/10.1002/zamm.200410211
6. Rohde, C. (2005). Phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy. Interfaces Free Bound., 7(1), 107--129. https://doi.org/10.4171/IFB/116
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  @article{rohde2005phase, author = {Rohde, Christian}, doi = {10.4171/IFB/116}, fjournal = {Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation}, issn = {1463-9963}, journal = {Interfaces Free Bound.}, mrclass = {35L65 (35L45 35L67 35Q72 74N99 82B26)}, mrnumber = {2126146 (2005k:35268)}, mrreviewer = {Nicole Turb{\'e}}, number = 1, owner = {szur}, pages = {107--129}, title = {Phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy}, url = {http://dx.doi.org/10.4171/IFB/116}, volume = 7, year = 2005 }
  Link
  http://dx.doi.org/10.4171/IFB/116
7. Gander, M. J., & Rohde, C. (2005). Nonlinear advection problems and overlapping Schwarz waveform relaxation. In Domain decomposition methods in science and engineering (Vol. 40, pp. 251--258). Springer. https://doi.org/10.1007/3-540-26825-1_23
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  @incollection{gander2005nonlinear, address = {Berlin}, author = {Gander, Martin J. and Rohde, Christian}, booktitle = {Domain decomposition methods in science and engineering}, doi = {10.1007/3-540-26825-1_23}, mrclass = {65M55}, mrnumber = {2235749}, owner = {szur}, pages = {251--258}, publisher = {Springer}, series = {Lect. Notes Comput. Sci. Eng.}, title = {Nonlinear advection problems and overlapping {S}chwarz waveform relaxation}, url = {http://dx.doi.org/10.1007/3-540-26825-1_23}, volume = 40, year = 2005 }
  Link
  http://dx.doi.org/10.1007/3-540-26825-1_23
8. Dedner, A., Kröner, D., Rohde, C., & Wesenberg, M. (2005). Radiation magnetohydrodynamics: analysis for model problems and efficient 3d-simulations for the full system. In Analysis and numerics for conservation laws (pp. 163--202). Springer. https://doi.org/10.1007/3-540-27907-5_8
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  BibTeX
  @incollection{dedner2005radiation, address = {Berlin}, author = {Dedner, A. and Kr{\"o}ner, D. and Rohde, C. and Wesenberg, M.}, booktitle = {Analysis and numerics for conservation laws}, doi = {10.1007/3-540-27907-5_8}, mrclass = {85A30 (35B35 35Q35 76W05 85-08)}, mrnumber = {2169928 (2006m:85002)}, mrreviewer = {Nina G. Khatiashvili}, owner = {szur}, pages = {163--202}, publisher = {Springer}, title = {Radiation magnetohydrodynamics: analysis for model problems and efficient 3d-simulations for the full system}, url = {http://dx.doi.org/10.1007/3-540-27907-5_8}, year = 2005 }
  Link
  http://dx.doi.org/10.1007/3-540-27907-5_8
2004
1. Dedner, A., Rohde, C., Schupp, B., & Wesenberg, M. (2004). A parallel, load-balanced MHD code on locally-adapted unstructured grids in 3d. Comput. Vis. Sci., 7(2), 79--96. https://doi.org/10.1007/s00791-004-0140-5
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  @article{dedner2004parallel, author = {Dedner, Andreas and Rohde, Christian and Schupp, Bernhard and Wesenberg, Matthias}, doi = {10.1007/s00791-004-0140-5}, fjournal = {Computing and Visualization in Science}, issn = {1432-9360}, journal = {Comput. Vis. Sci.}, mrclass = {76M12 (65M50 76W05 85A30)}, mrnumber = {2088784 (2006a:76075)}, mrreviewer = {Alexander M. Blokhin}, number = 2, owner = {szur}, pages = {79--96}, title = {A parallel, load-balanced {MHD} code on locally-adapted unstructured grids in 3d}, url = {http://dx.doi.org/10.1007/s00791-004-0140-5}, volume = 7, year = 2004 }
  Link
  http://dx.doi.org/10.1007/s00791-004-0140-5
2. Dedner, A., & Rohde, C. (2004). Numerical approximation of entropy solutions for hyperbolic integro-differential equations. Numer. Math., 97(3), 441--471. https://doi.org/10.1007/s00211-003-0502-9
  - BibTeX
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  BibTeX
  @article{dedner2004numerical, author = {Dedner, Andreas and Rohde, Christian}, coden = {NUMMA7}, doi = {10.1007/s00211-003-0502-9}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {45K05 (35L60 35Q35 65M06 65M15)}, mrnumber = {2059465 (2005f:45016)}, mrreviewer = {Guillaume Bal}, number = 3, owner = {szur}, pages = {441--471}, title = {Numerical approximation of entropy solutions for hyperbolic integro-differential equations}, url = {http://dx.doi.org/10.1007/s00211-003-0502-9}, volume = 97, year = 2004 }
  Link
  http://dx.doi.org/10.1007/s00211-003-0502-9
3. Rohde, C., & Thanh, M. D. (2004). Global existence for phase transition problems via a variational scheme. J. Hyperbolic Differ. Equ., 1(4), 747--768. https://doi.org/10.1142/S0219891604000329
  - BibTeX
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  BibTeX
  @article{rohde2004global, author = {Rohde, Christian and Thanh, Mai Duc}, doi = {10.1142/S0219891604000329}, fjournal = {Journal of Hyperbolic Differential Equations}, issn = {0219-8916}, journal = {J. Hyperbolic Differ. Equ.}, mrclass = {35K50 (35A35 74H20 74N99)}, mrnumber = {2111581 (2005k:35183)}, mrreviewer = {L. Hsiao}, number = 4, owner = {szur}, pages = {747--768}, title = {Global existence for phase transition problems via a variational scheme}, url = {http://dx.doi.org/10.1142/S0219891604000329}, volume = 1, year = 2004 }
  Link
  http://dx.doi.org/10.1142/S0219891604000329
2003
1. Kröner, D., Küther, M., Ohlberger, M., & Rohde, C. (2003). A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws. In Trends in nonlinear analysis (pp. 289--306). Springer.
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  @incollection{kroner2003posteriori, address = {Berlin}, author = {Kr{\"o}ner, Dietmar and K{\"u}ther, Marc and Ohlberger, Mario and Rohde, Christian}, booktitle = {Trends in nonlinear analysis}, mrclass = {65M15 (65M06 65M50 76M12)}, mrnumber = {1999102 (2004g:65117)}, owner = {szur}, pages = {289--306}, publisher = {Springer}, title = {A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws}, year = 2003 }
2. Dedner, A., Kröner, D., Rohde, C., Schnitzer, T., & Wesenberg, M. (2003). Comparison of finite volume and discontinuous Galerkin methods of higher order for systems of conservation laws in multiple space dimensions. In Geometric analysis and nonlinear partial differential equations (pp. 573--589). Springer.
  - BibTeX
  BibTeX
  @incollection{dedner2003comparison, address = {Berlin}, author = {Dedner, A. and Kr{\"o}ner, D. and Rohde, C. and Schnitzer, T. and Wesenberg, M.}, booktitle = {Geometric analysis and nonlinear partial differential equations}, mrclass = {65M06 (35L65 65M60 76M10 76M12)}, mrnumber = {2008357}, owner = {szur}, pages = {573--589}, publisher = {Springer}, title = {Comparison of finite volume and discontinuous {G}alerkin methods of higher order for systems of conservation laws in multiple space dimensions}, year = 2003 }
3. Rohde, C., & Zajaczkowski, W. (2003). On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation. Appl. Math., 48(4), 257--277. https://doi.org/10.1023/A:1026010631074
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  BibTeX
  @article{rohde2003cauchy, author = {Rohde, C. and Zaj{\polhk{a}}czkowski, W.}, doi = {10.1023/A:1026010631074}, fjournal = {Applications of Mathematics}, issn = {0862-7940}, journal = {Appl. Math.}, mrclass = {35Q35 (35L60 35Q60 76N10 76W05)}, mrnumber = {1994377 (2004f:35147)}, mrreviewer = {Paolo Secchi}, number = 4, owner = {szur}, pages = {257--277}, title = {On the {C}auchy problem for the equations of ideal compressible {MHD} fluids with radiation}, url = {http://dx.doi.org/10.1023/A:1026010631074}, volume = 48, year = 2003 }
  Link
  http://dx.doi.org/10.1023/A:1026010631074
4. Freistühler, H., & Rohde, C. (2003). The bifurcation analysis of the MHD Rankine-Hugoniot equations for a perfect gas. Phys. D, 185(2), 78--96. https://doi.org/10.1016/S0167-2789(03)00206-9
  - BibTeX
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  BibTeX
  @article{freistuhler2003bifurcation, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, coden = {PDNPDT}, doi = {10.1016/S0167-2789(03)00206-9}, fjournal = {Physica D. Nonlinear Phenomena}, issn = {0167-2789}, journal = {Phys. D}, mrclass = {76L05 (35B32 35L67 76N15 76W05)}, mrnumber = {2014893 (2004k:76079)}, mrreviewer = {Alastair M. Rucklidge}, number = 2, owner = {szur}, pages = {78--96}, title = {The bifurcation analysis of the {MHD} {R}ankine-{H}ugoniot equations for a perfect gas}, url = {http://dx.doi.org/10.1016/S0167-2789(03)00206-9}, volume = 185, year = 2003 }
  Link
  http://dx.doi.org/10.1016/S0167-2789(03)00206-9
5. Dedner, A., Rohde, C., & Wesenberg, M. (2003). Efficient higher-order finite volume schemes for (real gas) magnetohydrodynamics. In Hyperbolic problems: theory, numerics, applications (pp. 499--508). Springer.
  - BibTeX
  BibTeX
  @incollection{dedner2003efficient, address = {Berlin}, author = {Dedner, Andreas and Rohde, Christian and Wesenberg, Matthias}, booktitle = {Hyperbolic problems: theory, numerics, applications}, mrclass = {65M06 (35Q35 65M50 76M12)}, mrnumber = {2053199}, owner = {szur}, pages = {499--508}, publisher = {Springer}, title = {Efficient higher-order finite volume schemes for (real gas) magnetohydrodynamics}, year = 2003 }
6. Dedner, A., Rohde, C., & Wesenberg, M. (2003). A new approach to divergence cleaning in magnetohydrodynamic simulations. In Hyperbolic problems: theory, numerics, applications (pp. 509--518). Springer.
  - BibTeX
  BibTeX
  @incollection{dedner2003approach, address = {Berlin}, author = {Dedner, Andreas and Rohde, Christian and Wesenberg, Matthias}, booktitle = {Hyperbolic problems: theory, numerics, applications}, mrclass = {76M25 (76W05)}, mrnumber = {2053200}, owner = {szur}, pages = {509--518}, publisher = {Springer}, title = {A new approach to divergence cleaning in magnetohydrodynamic simulations}, year = 2003 }
2002
1. Dedner, A., & Rohde, C. (2002). FV-schemes for a scalar model problem of radiation magnetohydrodynamics. In Finite volumes for complex applications, III (Porquerolles, 2002) (pp. 165--172). Hermes Sci. Publ., Paris.
  - BibTeX
  BibTeX
  @incollection{dedner2002fvschemes, author = {Dedner, Andreas and Rohde, Christian}, booktitle = {Finite volumes for complex applications, {III} ({P}orquerolles, 2002)}, mrclass = {65M06 (76W05 78A40 85A30)}, mrnumber = {2007414}, owner = {szur}, pages = {165--172}, publisher = {Hermes Sci. Publ., Paris}, title = {F{V}-schemes for a scalar model problem of radiation magnetohydrodynamics}, year = 2002 }
2. Freistühler, H., & Rohde, C. (2002). Numerical computation of viscous profiles for hyperbolic conservation laws. Math. Comp., 71(239), 1021--1042 (electronic). https://doi.org/10.1090/S0025-5718-01-01340-0
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  BibTeX
  @article{freistuhler2002numerical, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, coden = {MCMPAF}, doi = {10.1090/S0025-5718-01-01340-0}, fjournal = {Mathematics of Computation}, issn = {0025-5718}, journal = {Math. Comp.}, mrclass = {65M99 (35L65 76M25 76N10 76W05)}, mrnumber = {1898744 (2003f:65178)}, mrreviewer = {Gholam-Ali Zakeri}, number = 239, owner = {szur}, pages = {1021--1042 (electronic)}, title = {Numerical computation of viscous profiles for hyperbolic conservation laws}, url = {http://dx.doi.org/10.1090/S0025-5718-01-01340-0}, volume = 71, year = 2002 }
  Link
  http://dx.doi.org/10.1090/S0025-5718-01-01340-0
3. Ohlberger, M., & Rohde, C. (2002). Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems. IMA J. Numer. Anal., 22(2), 253--280. https://doi.org/10.1093/imanum/22.2.253
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  BibTeX
  @article{ohlberger2002adaptive, author = {Ohlberger, Mario and Rohde, Christian}, coden = {IJNADN}, doi = {10.1093/imanum/22.2.253}, fjournal = {IMA Journal of Numerical Analysis}, issn = {0272-4979}, journal = {IMA J. Numer. Anal.}, mrclass = {65M06 (65M15 76M12)}, mrnumber = {1897409 (2003e:65152)}, number = 2, owner = {szur}, pages = {253--280}, title = {Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems}, url = {http://dx.doi.org/10.1093/imanum/22.2.253}, volume = 22, year = 2002 }
  Link
  http://dx.doi.org/10.1093/imanum/22.2.253
4. Lefloch, P. G., Mercier, J. M., & Rohde, C. (2002). Fully discrete, entropy conservative schemes of arbitrary order. SIAM J. Numer. Anal., 40(5), 1968--1992 (electronic). https://doi.org/10.1137/S003614290240069X
  - BibTeX
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  BibTeX
  @article{lefloch2002fully, author = {Lefloch, P. G. and Mercier, J. M. and Rohde, C.}, doi = {10.1137/S003614290240069X}, fjournal = {SIAM Journal on Numerical Analysis}, issn = {0036-1429}, journal = {SIAM J. Numer. Anal.}, mrclass = {65M06 (35L65 35M10)}, mrnumber = {1950629 (2003k:65088)}, mrreviewer = {Dennis C. Jespersen}, number = 5, owner = {szur}, pages = {1968--1992 (electronic)}, title = {Fully discrete, entropy conservative schemes of arbitrary order}, url = {http://dx.doi.org/10.1137/S003614290240069X}, volume = 40, year = 2002 }
  Link
  http://dx.doi.org/10.1137/S003614290240069X
2001
1. Haasdonk, B., Kröner, D., & Rohde, C. (2001). Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids. Numer. Math., 88(3), 459--484. https://doi.org/10.1007/s211-001-8011-x
  - BibTeX
  BibTeX
  @article{haasdonk2001convergence, author = {Haasdonk, B. and Kröner, D. and Rohde, C.}, coden = {NUMMA7}, doi = {10.1007/s211-001-8011-x}, file = {:/afs/.mathe/public/www/ians/am/Haasdonk/publications/HKR01.pdf:PDF}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M06}, mrnumber = {1835467 (2002c:65133)}, mrreviewer = {Kenneth H. Karlsen}, number = 3, owner = {szur}, pages = {459--484}, title = {Convergence of a staggered {L}ax-{F}riedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids}, volume = 88, year = 2001 }
2. Freistühler, H., Fries, C., & Rohde, C. (2001). Existence, bifurcation, and stability of profiles for classical and non-classical shock waves. In Ergodic theory, analysis, and efficient simulation of dynamical systems (pp. 287--309, 814). Springer.
  - BibTeX
  BibTeX
  @incollection{freistuhler2001existence, address = {Berlin}, author = {Freist{\"u}hler, Heinrich and Fries, Christian and Rohde, Christian}, booktitle = {Ergodic theory, analysis, and efficient simulation of dynamical systems}, mrclass = {35L67 (35B35 35L65 35Q35 76L05 76W05)}, mrnumber = {1850311 (2002g:35150)}, mrreviewer = {Kenji Nishihara}, owner = {szur}, pages = {287--309, 814}, publisher = {Springer}, title = {Existence, bifurcation, and stability of profiles for classical and non-classical shock waves}, year = 2001 }
3. Dedner, A., Kröner, D., Rohde, C., & Wesenberg, M. (2001). Godunov-type schemes for the MHD equations. In Godunov methods (Oxford, 1999) (pp. 209--216). Kluwer/Plenum, New York.
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  BibTeX
  @incollection{dedner2001godunovtype, author = {Dedner, A. and Kr{\"o}ner, D. and Rohde, C. and Wesenberg, M.}, booktitle = {Godunov methods ({O}xford, 1999)}, mrclass = {76M20 (76W05)}, mrnumber = {1963594}, owner = {szur}, pages = {209--216}, publisher = {Kluwer/Plenum, New York}, title = {Godunov-type schemes for the {MHD} equations}, year = 2001 }
4. Freistühler, H., & Rohde, C. (2001). A numerical study on viscous profiles of MHD shock waves. In Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000) (Vol. 141, pp. 399--408). Birkhäuser.
  - BibTeX
  BibTeX
  @incollection{freistuhler2001numerical, address = {Basel}, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, booktitle = {Hyperbolic problems: theory, numerics, applications, {V}ol. {I}, {II} ({M}agdeburg, 2000)}, mrclass = {76M25 (35Q35 76L05 76W05)}, mrnumber = {1882941}, owner = {szur}, pages = {399--408}, publisher = {Birkh\"auser}, series = {Internat. Ser. Numer. Math., 140}, title = {A numerical study on viscous profiles of {MHD} shock waves}, volume = 141, year = 2001 }
5. LeFloch, P. G., & Rohde, C. (2001). Zero diffusion-dispersion limits for self-similar Riemann solutions to hyperbolic systems of conservation laws. Indiana Univ. Math. J., 50(4), 1707--1743. https://doi.org/10.1512/iumj.2001.50.2057
  - BibTeX
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  BibTeX
  @article{lefloch2001diffusiondispersion, author = {LeFloch, Philippe G. and Rohde, Christian}, coden = {IUMJAB}, doi = {10.1512/iumj.2001.50.2057}, fjournal = {Indiana University Mathematics Journal}, issn = {0022-2518}, journal = {Indiana Univ. Math. J.}, mrclass = {35L65}, mrnumber = {1889079 (2002k:35194)}, mrreviewer = {Denis Serre}, number = 4, owner = {szur}, pages = {1707--1743}, title = {Zero diffusion-dispersion limits for self-similar {R}iemann solutions to hyperbolic systems of conservation laws}, url = {http://dx.doi.org/10.1512/iumj.2001.50.2057}, volume = 50, year = 2001 }
  Link
  http://dx.doi.org/10.1512/iumj.2001.50.2057
6. Hillen, T., Rohde, C., & Lutscher, F. (2001). Existence of weak solutions for a hyperbolic model of chemosensitive movement. J. Math. Anal. Appl., 260(1), 173--199. https://doi.org/10.1006/jmaa.2001.7447
  - BibTeX
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  BibTeX
  @article{hillen2001existence, author = {Hillen, Thomas and Rohde, Christian and Lutscher, Frithjof}, coden = {JMANAK}, doi = {10.1006/jmaa.2001.7447}, fjournal = {Journal of Mathematical Analysis and Applications}, issn = {0022-247X}, journal = {J. Math. Anal. Appl.}, mrclass = {35Q80 (35A35 35D05 35L60 92C17)}, mrnumber = {1843975 (2003c:35153)}, number = 1, owner = {szur}, pages = {173--199}, title = {Existence of weak solutions for a hyperbolic model of chemosensitive movement}, url = {http://dx.doi.org/10.1006/jmaa.2001.7447}, volume = 260, year = 2001 }
  Link
  http://dx.doi.org/10.1006/jmaa.2001.7447
7. Haasdonk, B., Kröner, D., & Rohde, C. (2001). Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids. Numer. Math., 88(3), 459--484. https://doi.org/10.1007/s211-001-8011-x
  - BibTeX
  - Link
  BibTeX
  @article{haasdonk2001convergence, author = {Haasdonk, B. and Kr{\"o}ner, D. and Rohde, C.}, coden = {NUMMA7}, doi = {10.1007/s211-001-8011-x}, file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Haasdonk2001a_www_preprint_StgLxF_convergence.pdf:PDF}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M06}, mrnumber = {MR1835467 (2002c:65133)}, mrreviewer = {Kenneth H. Karlsen}, number = 3, owner = {haasdonk}, pages = {459--484}, title = {Convergence of a staggered {L}ax-{F}riedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids}, url = {http://dx.doi.org/10.1007/s211-001-8011-x}, volume = 88, year = 2001 }
  Link
  http://dx.doi.org/10.1007/s211-001-8011-x
8. Dedner, A., Kröner, D., Rohde, C., & Wesenberg, M. (2001). MHD instabilities arising in solar physics: a numerical approach. In Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000) (Vol. 141, pp. 277--286). Birkhäuser.
  - BibTeX
  BibTeX
  @incollection{dedner2001instabilities, address = {Basel}, author = {Dedner, Andreas and Kr{\"o}ner, Dietmar and Rohde, Christian and Wesenberg, Matthias}, booktitle = {Hyperbolic problems: theory, numerics, applications, {V}ol. {I}, {II} ({M}agdeburg, 2000)}, mrclass = {85A30 (76E25 76W05 85-08)}, mrnumber = {1882928}, owner = {szur}, pages = {277--286}, publisher = {Birkh\"auser}, series = {Internat. Ser. Numer. Math., 140}, title = {M{HD} instabilities arising in solar physics: a numerical approach}, volume = 141, year = 2001 }
2000
1. Lefloch, P. G., & Rohde, C. (2000). High-order schemes, entropy inequalities, and nonclassical shocks. SIAM J. Numer. Anal., 37(6), 2023--2060 (electronic). https://doi.org/10.1137/S0036142998345256
  - BibTeX
  - Link
  BibTeX
  @article{lefloch2000highorder, author = {Lefloch, Philippe G. and Rohde, Christian}, doi = {10.1137/S0036142998345256}, fjournal = {SIAM Journal on Numerical Analysis}, issn = {0036-1429}, journal = {SIAM J. Numer. Anal.}, mrclass = {65M12 (35L67 76L05 76M20)}, mrnumber = {1766858 (2001e:65139)}, mrreviewer = {Eun-Jae Park}, number = 6, owner = {szur}, pages = {2023--2060 (electronic)}, title = {High-order schemes, entropy inequalities, and nonclassical shocks}, url = {http://dx.doi.org/10.1137/S0036142998345256}, volume = 37, year = 2000 }
  Link
  http://dx.doi.org/10.1137/S0036142998345256
1999
1. Dedner, A., Rohde, C., & Wesenberg, M. (1999). A MHD-simulation in solar physics. In Finite volumes for complex applications II (pp. 491--498). Hermes Sci. Publ., Paris.
  - BibTeX
  BibTeX
  @incollection{dedner1999mhdsimulation, author = {Dedner, A. and Rohde, C. and Wesenberg, M.}, booktitle = {Finite volumes for complex applications {II}}, mrclass = {65M50 (76W05 85A30)}, mrnumber = {2062167}, owner = {szur}, pages = {491--498}, publisher = {Hermes Sci. Publ., Paris}, title = {A {MHD}-simulation in solar physics}, year = 1999 }
2. Freistühler, H., & Rohde, C. (1999). Numerical methods for viscous profiles of non-classical shock waves. In Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich, 1998) (Vol. 129, pp. 333--342). Birkhäuser.
  - BibTeX
  BibTeX
  @incollection{freistuhler1999numerical, address = {Basel}, author = {Freist{\"u}hler, Heinrich and Rohde, Christian}, booktitle = {Hyperbolic problems: theory, numerics, applications, {V}ol. {I} ({Z}\"urich, 1998)}, mrclass = {65M30 (76L05 76M25 76W05)}, mrnumber = {1717203 (2000i:65140)}, mrreviewer = {Shi Jin}, owner = {szur}, pages = {333--342}, publisher = {Birkh\"auser}, series = {Internat. Ser. Numer. Math.}, title = {Numerical methods for viscous profiles of non-classical shock waves}, volume = 129, year = 1999 }
1998
1. Rohde, C. (1998). Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2D. Numer. Math., 81(1), 85--123. https://doi.org/10.1007/s002110050385
  - BibTeX
  - Link
  BibTeX
  @article{rohde1998upwind, author = {Rohde, Christian}, coden = {NUMMA7}, doi = {10.1007/s002110050385}, fjournal = {Numerische Mathematik}, issn = {0029-599X}, journal = {Numer. Math.}, mrclass = {65M60 (35L65 76M25 76N15)}, mrnumber = {1657726 (99j:65174)}, mrreviewer = {Riccardo Fazio}, number = 1, owner = {szur}, pages = {85--123}, title = {Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2{D}}, url = {http://dx.doi.org/10.1007/s002110050385}, volume = 81, year = 1998 }
  Link
  http://dx.doi.org/10.1007/s002110050385
2. Rohde, C. (1998). Entropy solutions for weakly coupled hyperbolic systems in several space dimensions. Z. Angew. Math. Phys., 49(3), 470--499. https://doi.org/10.1007/s000000050102
  - BibTeX
  - Link
  BibTeX
  @article{rohde1998entropy, author = {Rohde, Christian}, coden = {AZMPA8}, doi = {10.1007/s000000050102}, fjournal = {Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math\'ematiques et de Physique Appliqu\'ees}, issn = {0044-2275}, journal = {Z. Angew. Math. Phys.}, mrclass = {35L60 (35L65)}, mrnumber = {1629553 (99e:35133)}, mrreviewer = {Ivan Stra{\v{s}}kraba}, number = 3, owner = {szur}, pages = {470--499}, title = {Entropy solutions for weakly coupled hyperbolic systems in several space dimensions}, url = {http://dx.doi.org/10.1007/s000000050102}, volume = 49, year = 1998 }
  Link
  http://dx.doi.org/10.1007/s000000050102

Teaching

Winter term 2022/23:
Summer term 2022:
Winter term 2021/22:
- Numerische Mathematik 1
- Stochastik und Angewandte Mathematik für das Lehramt (zusammen mit M. Griesemer)
- Masterseminar Mathematische Modellierung: Grenzflächendynamik: scharf oder diffus?
Summer term 2021:
- Mathematische Methoden in der Strömungsmechanik (zusammen mit C.-D. Munz)
- Mathematische Modellierung
- Proseminar Numerik für Data Sciences
Winter term 2020/21:
Summer term 2020: none
Winter term 2019/20:
- Introduction to the numerics of partial differential equations,
- Stochastik und Angewandte Mathematik sowie
- MSc-Seminar für Mehrphasenströmungen

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Christian Rohde

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