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Rohde, Christian

Prof. Dr.

Christian Rohde

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

Contact

+49 711 685-65524
+49 711 685-65599
Email

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.131

Office Hours

Fridays 13:00 - 14:00 and by appointment

Publications

2020
1. L. Ostrowski and C. Rohde, “Compressible multicomponent flow in porous media with Maxwell-Stefan diffusion,” Math. Meth. Appl. Sci., vol. 43, no. 7, Art. no. 7, 2020, doi: 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. C. Rohde and L. von Wolff, “A Ternary Cahn-Hilliard Navier-Stokes model for two phase flow with precipitation and dissolution,” accepted for publication in Math. Model Meth. Appl. Sci., 2020, [Online]. Available: https://arxiv.org/abs/1912.09181.
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  @article{rohde2019ternary, archiveprefix = {arXiv}, author = {Rohde, Christian and von Wolff, Lars}, eprint = {1912.09181}, journal = {accepted for publication in Math. Model Meth. Appl. Sci.}, primaryclass = {math.AP}, title = {A Ternary Cahn-Hilliard Navier-Stokes model for two phase flow with precipitation and dissolution}, url = {https://arxiv.org/abs/1912.09181}, year = 2020 }
  Link
  https://arxiv.org/abs/1912.09181
3. J. Magiera, D. Ray, J. S. Hesthaven, and C. Rohde, “Constraint-aware neural networks for Riemann problems,” J. Comput. Phys., vol. 409, no. 109345, Art. no. 109345, 2020, doi: 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
4. J. Giesselmann, F. Meyer, and C. Rohde, “A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method,” IMA J. Numer. Anal., vol. 40, no. 2, Art. no. 2, 2020, doi: 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
5. C. Rohde and L. von Wolff, “Homogenization of non-local Navier-Stokes-Korteweg equations for compressible liquid-vapour flow in porous media,” accepted for publication in SIAM J. Math. Anal., 2020, [Online]. Available: https://arxiv.org/abs/1902.07100.
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  @article{rohdevwolff20, author = {Rohde, Christian and von Wolff, Lars}, journal = {accepted for publication in SIAM J. Math. Anal.}, title = {Homogenization of non-local Navier-Stokes-Korteweg equations for compressible liquid-vapour flow in porous media}, url = {https://arxiv.org/abs/1902.07100}, year = 2020 }
  Link
  https://arxiv.org/abs/1902.07100
6. J. Giesselmann, F. Meyer, and C. Rohde, “An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws,” in Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018, 2020, vol. 10, pp. 449–456, [Online]. Available: 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
7. C. Rohde and H. Tang, “On the stochastic Dullin-Gottwald-Holm equation: Global existence and wave-breaking phenomena,” accepted for publication in NoDEA Nonlinear Differential Equations Appl., 2020, [Online]. Available: https://arxiv.org/abs/2003.07206.
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  @article{RohdeTang2020b, author = {Rohde, Christian and Tang, Hao}, journal = {accepted for publication in NoDEA Nonlinear Differential Equations Appl.}, title = {On the stochastic Dullin-Gottwald-Holm equation: Global existence and wave-breaking phenomena}, url = {https://arxiv.org/abs/2003.07206}, year = 2020 }
  Link
  https://arxiv.org/abs/2003.07206
8. J. Giesselmann, F. Meyer, and C. Rohde, “A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws,” BIT Numerical Mathematics, vol. 60, no. 3, Art. no. 3, 2020, doi: 10.1007/s10543-019-00794-z.
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  @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 }
9. A. Beck, J. Dürrwächter, T. Kuhn, F. Meyer, C.-D. Munz, and C. Rohde, “$hp$-Multilevel Monte Carlo methods for uncertainty quantification of compressible flows,” SIAM J. Sci. Comput., vol. 42, no. 4, Art. no. 4, 2020, doi: 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
10. A. Armiti-Juber and C. Rohde, “On the well-posedness of a nonlinear fourth-order extension of Richards’ equation,” J. Math. Anal. Appl., vol. 487, no. 2, Art. no. 2, 2020, doi: 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 }
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  http://www.sciencedirect.com/science/article/pii/S0022247X20301670
11. L. Ostrowski, F. C. Massa, and C. Rohde, “A phase field approach to compressible droplet impingement,” in Droplet Interactions and Spray Processes, Cham, 2020, pp. 113–126, [Online]. Available: 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
12. C. Rohde and H. Tang, “On a stochastic Camassa-Holm type equation with higher order nonlinearities,” accepted for publication in J. Dynam. Differential Equations, 2020, [Online]. Available: https://arxiv.org/abs/2001.05754.
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  @article{rohde2020stochastic, archiveprefix = {arXiv}, author = {Rohde, Christian and Tang, Hao}, eprint = {2001.05754}, journal = {accepted for publication in J. Dynam. Differential Equations}, primaryclass = {math.AP}, title = {On a stochastic Camassa-Holm type equation with higher order nonlinearities}, url = {https://arxiv.org/abs/2001.05754}, year = 2020 }
  Link
  https://arxiv.org/abs/2001.05754
13. S. Burbulla and C. Rohde, “A fully conforming finite volume approach to two-phase flow in fractured porous media,” in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, Cham, 2020, pp. 547–555, doi: 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
14. L. Ostrowski and C. Rohde, “Phase field modelling for compressible droplet impingement,” in Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018, 2020, vol. 10, pp. 586–593, [Online]. Available: https://www.aimsciences.org/fileAIMS/cms/news/info/upload//c0904f1f-97d5-451f-b068-25f1612b6852.pdf.
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  @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
15. D. Alonso-Orán, C. Rohde, and H. Tang, “A local-in-time theory for singular SDEs with applications to fluid models with transport noise.” 2020, [Online]. Available: https://arxiv.org/abs/2010.09972.
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  @misc{alonsoorán2020localintime, archiveprefix = {arXiv}, author = {Alonso-Orán, Diego and Rohde, Christian and Tang, Hao}, eprint = {2010.09972}, primaryclass = {math.PR}, title = {A local-in-time theory for singular SDEs with applications to fluid models with transport noise}, url = {https://arxiv.org/abs/2010.09972}, year = 2020 }
  Link
  https://arxiv.org/abs/2010.09972
16. T. Hitz, J. Keim, C.-D. Munz, and C. Rohde, “A parabolic relaxation model for the Navier-Stokes-Korteweg equations,” J. Comput. Phys, vol. 421, p. 109714, 2020, doi: 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. J. Giesselmann, F. Meyer, and C. Rohde, “Error control for statistical solutions,” 2019, [Online]. Available: https://arxiv.org/abs/1912.04323.
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  @article{GMR2019error, author = {Giesselmann, J. and Meyer, F. and Rohde, C.}, title = {Error control for statistical solutions}, url = {https://arxiv.org/abs/1912.04323}, year = 2019 }
  Link
  https://arxiv.org/abs/1912.04323
2. R. M. Colombo, P. G. LeFloch, C. Rohde, and K. Trivisa, “Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics,” Oberwohlfach Rep., no. 16, Art. no. 16, 2019, [Online]. Available: 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
3. T. Kuhn, J. Dürrwächter, F. Meyer, A. Beck, C. Rohde, and C.-D. Munz, “Uncertainty quantification for direct aeroacoustic simulations of cavity flows,” J. Theor. Comput. Acoust., vol. 27, no. 1, 1850044, Art. no. 1, 1850044, 2019, doi: 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, 1850044}, 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
4. V. Sharanya, G. P. R. Sekhar, and C. Rohde, “Surfactant-induced migration of a spherical droplet in non-isothermal Stokes flow,” Phys. Fluids, no. 31, 012110, Art. no. 31, 012110, 2019, doi: 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 = {https://doi.org/10.1063/1.5064694}, journal = {Phys. Fluids}, number = {31, 012110}, title = {Surfactant-induced migration of a spherical droplet in non-isothermal Stokes flow}, url = {https://doi.org/10.1063/1.5064694}, year = 2019 }
  Link
  https://doi.org/10.1063/1.5064694
5. A. Armiti-Juber and C. Rohde, “On Darcy-and Brinkman-type models for two-phase flow in asymptotically flat domains,” Comput. Geosci., vol. 23, no. 2, Art. no. 2, 2019, doi: 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 }
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  https://link.springer.com/article/10.1007/s10596-018-9756-2
6. D. Seus, F. A. Radu, and C. Rohde, “A linear domain decomposition method for two-phase flow in porous media,” Numerical Mathematics and Advanced Applications ENUMATH 2017, pp. 603–614, 2019, doi: https://doi.org/10.1007/978-3-319-96415-7_55.
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  @article{seus2019linear, abstract = {This article is a follow up of our submitted paper (D. Seus et al, Comput Methods Appl Mech Eng 333:331--355, 2018) in which a decomposition of the Richards equation along two soil layers was discussed. A decomposed problem was formulated and a decoupling and linearisation technique was presented to solve the problem in each time step in a fixed point type iteration. This article extends these ideas to the case of two-phase in porous media and the convergence of the proposed domain decomposition method is rigorously shown."}, author = {Seus, David and Radu, Florin A. and Rohde, Christian}, doi = {https://doi.org/10.1007/978-3-319-96415-7_55}, editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin}, isbn = {978-3-319-96415-7}, journal = {Numerical Mathematics and Advanced Applications ENUMATH 2017}, pages = {603-614}, publisher = {Springer International Publishing}, title = {A linear domain decomposition method for two-phase flow in porous media}, url = {https://www.springerprofessional.de/a-linear-domain-decomposition-method-for-two-phase-flow-in-porou/16377432}, year = 2019 }
  Link
  https://www.springerprofessional.de/a-linear-domain-decomposition-method-for-two-phase-flow-in-porou/16377432
7. J. Dürrwächter, F. Meyer, T. Kuhn, A. Beck, C.-D. Munz, and C. Rohde, “A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations,” 2019, [Online]. Available: 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.
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  BibTeX
  @article{Duerrwaechter2019, author = {D{\"u}rrw{\"a}chter, Jakob and Meyer, Fabian and Kuhn, Thomas and Beck, Andrea and Munz, Claus-Dieter and Rohde, Christian}, 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}, year = 2019 }
  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
8. M. Köppel et al., “Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,” Comput. Geosci., vol. 2, no. 23, Art. no. 23, 2019, doi: https://doi.org/10.1007/s10596-018-9785-x.
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  BibTeX
  @article{koppel2017comparison, 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 methods� 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, B. and Nowak, W. and Pfl\{"u}ger, D. and Rohde, C.}, doi = {https://doi.org/10.1007/s10596-018-9785-x}, journal = {Comput. Geosci.}, number = 23, owner = {santinge}, pages = {339-354}, publisher = {Springer International Publishing}, 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 = 2, year = 2019 }
  Link
  https://doi.org/10.1007/s10596-018-9785-x
2018
1. D. Seus, I. S. Pop, C. Rohde, K. Mitra, and F. Radu, “A linear domain decompostition method for partially saturated flow in porous media,” Comput. Methods Appl. Mech. Eng., vol. 333, pp. 331–355, 2018, doi: 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
2. S. Fechter, C.-D. Munz, C. Rohde, and C. Zeiler, “Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension,” Comput. & Fluids, vol. 169, pp. 169–185, 2018, doi: http://dx.doi.org/10.1016/j.compfluid.2017.03.026.
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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
3. V. Sharanya, G. P. R. Sekhar, and C. Rohde, “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, vol. 107, pp. 82–103, 2018, doi: 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
4. C. Rohde and C. Zeiler, “On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension,” Z. Angew. Math. Phys., no. 3, Art. no. 3, 2018, doi: https://doi.org/10.1007/s00033-018-0958-1.
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  @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
5. C. Chalons, J. Magiera, C. Rohde, and M. Wiebe, “A finite-volume tracking scheme for two-phase compressible flow,” Springer Proc. Math. Stat., pp. 309--322, 2018, doi: https://doi.org/10.1007/978-3-319-91545-6_25.
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  @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
6. C. Rohde, “Fully resolved compressible two-phase flow : modelling, analytical and numerical issues,” in New trends and results in mathematical description of fluid flows, M. Bulicek, E. Feireisl, and M. Pokorný, Eds. Basel: Birkhäuser, 2018, pp. 115–181.
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  @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
7. J. Magiera and C. Rohde, “A particle-based multiscale solver for compressible liquid-vapor flow,” Springer Proc. Math. Stat., pp. 291--304, 2018, doi: 10.1007/978-3-319-91548-7_23.
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  @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. S. Fechter, C.-D. Munz, C. Rohde, and C. Zeiler, “A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension,” J. Comput. Phys., vol. 336, pp. 347–374, 2017, doi: 10.1016/j.jcp.2017.02.001.
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  @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 = {MAY 1}, 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. M. Köppel, I. Kröker, and C. Rohde, “Intrusive uncertainty quantification for hyperbolic-elliptic systems governing two-phase flow in heterogeneous porous media,” Comput. Geosci., vol. 21, pp. 807–832, 2017, doi: 10.1007/s10596-017-9662-z.
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  @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. C. Chalons, C. Rohde, and M. Wiebe, “A finite volume method for undercompressive shock waves in two space dimensions,” ESAIM Math. Model. Numer. Anal., vol. 51, no. 5, Art. no. 5, 2017, doi: https://doi.org/10.1051/m2an/2017027.
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  @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 = {September-October 2017}, 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
2016
1. M. Dumbser, G. Gassner, C. Rohde, and S. Roller, “Preface to the special issue ``Recent Advances in Numerical Methods for Hyperbolic Partial Differential Equations’’,” Appl. Math. Comput., vol. 272, no. part 2, Art. no. part 2, 2016, doi: 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. J. Magiera, C. Rohde, and I. Rybak, “A hyperbolic-elliptic model problem for coupled surface-subsurface flow,” Transp. Porous Media, vol. 114, pp. 425–455, 2016, doi: 10.1007/S11242-015-0548-Z.
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  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 }
3. V. Sharanya, G. P. Raja Sekhar, and C. Rohde, “Bed of polydisperse viscous spherical drops under thermocapillary effects,” Z. Angew. Math. Phys., vol. 67, no. 4, Art. no. 4, 2016, doi: 10.1007/s00033-016-0699-y.
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  @article{sharanya2016polydisperse, abstract = {Viscous flow past an ensemble of polydisperse spherical drops is investigated under thermocapillary effects. We assume that the collection of spherical drops behaves as a porous media and estimates the hydrodynamic interactions analytically via the so- called cell model that is defined around a specific representative particle. In this method, the hydrodynamic interactions are assumed to be accounted by suitable boundary conditions on a fictitious fluid envelope surrounding the representative particle. The force calculated on this representative particle will then be extended to a bed of spherical drops visualized as a Darcy porous bed. Thus, the ``effective bed permeability'' of such a porous bed will be computed as a function of various parameters and then will be compared with Carman--Kozeny relation. We use cell model approach to a packed bed of spherical drops of uniform size (monodisperse spherical drops) and then extend the work for a packed bed of polydisperse spherical drops, for a specific parameters. Our results show a good agreement with the Carman--Kozeny relation for the case of monodisperse spherical drops. The prediction of overall bed permeability using our present model agrees well with the Carman--Kozeny relation when the packing size distribution is narrow, whereas a small deviation can be noted when the size distribution becomes broader.}, author = {Sharanya, V. and Raja Sekhar, G. P. and Rohde, Christian}, doi = {10.1007/s00033-016-0699-y}, issn = {1420-9039}, journal = {Z. Angew. Math. Phys.}, number = 4, owner = {szur}, pages = 101, title = {Bed of polydisperse viscous spherical drops under thermocapillary effects}, url = {http://dx.doi.org/10.1007/s00033-016-0699-y}, volume = 67, year = 2016 }
  Link
  http://dx.doi.org/10.1007/s00033-016-0699-y
4. M. Redeker, I. S. Pop, and C. Rohde, “Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous Media,” IMA J. Appl. Math., vol. 81(5), pp. 898–939, 2016, doi: 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
5. I. Dragomirescu, K. Eisenschmidt, C. Rohde, and B. Weigand, “Perturbation solutions for the finite radially symmetric Stefan problem,” Inter. J. Thermal Sci., vol. 104, pp. 386–395, 2016, doi: https://doi.org/10.1016/j.ijthermalsci.2016.01.019.
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  @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
6. M. Köppel and C. Rohde, “Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media,” PAMM Proc. Appl. Math. Mech., vol. 16, no. 1, Art. no. 1, 2016, doi: 10.1002/pamm.201610363.
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  @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
7. D. Diehl, J. Kremser, D. Kröner, and C. Rohde, “Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions,” Appl. Math. Comput., vol. 272, no. 2, Art. no. 2, 2016, doi: 10.1016/j.amc.2015.09.080.
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  @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
8. R. M. Colombo, P. G. LeFloch, and C. Rohde, “Hyperbolic techniques in Modelling, Analysis and Numerics,” Oberwolfach Reports, vol. 13, pp. 1683–1751, 2016, doi: 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
9. F. Betancourt and C. Rohde, “Finite-volume schemes for Friedrichs systems with involutions,” App. Math. Comput., vol. 272, Part 2, pp. 420–439, 2016, doi: 10.1016/j.amc.2015.03.050.
  - BibTeX
  - Link
  BibTeX
  @article{BetancourtRohde16, abstract = {In applications solutions of systems of hyperbolic balance laws often have to satisfy additional side conditions. We consider initial value problems for the general class of Friedrichs systems where the solutions are constrained by differential conditions given in the form of involutions. These occur in particular in electrodynamics, electro- and magnetohydrodynamics as well as in elastodynamics. Neglecting the involution on the discrete level typically leads to instabilities. To overcome this problem in electrodynamical applications it has been suggested in Munz et al. (2000) to solve an extended system. Here we suggest an extended formulation to the general class of constrained Friedrichs systems. It is proven for explicit Finite-Volume schemes that the discrete solution of the extended system converges to the weak solution of the original system for vanishing discretization and extension parameter under appropriate scalings. Moreover we show that the involution is weakly satisfied in the limit. The proofs rely on a reformulation of the extension as a relaxation-type approximation and careful use of the convergence theory for finite-volume methods for systems of Friedrichs type. Numerical experiments illustrate our analytical results.}, author = {Betancourt, F. and Rohde, C.}, doi = {10.1016/j.amc.2015.03.050}, journal = {App. Math. Comput.}, owner = {seusdd}, pages = {420-439}, title = {Finite-volume schemes for Friedrichs systems with involutions}, url = {https://doi.org/10.1016/j.amc.2015.03.050}, volume = {272, Part 2}, year = 2016 }
  Link
  https://doi.org/10.1016/j.amc.2015.03.050
2015
1. I. Rybak, J. Magiera, R. Helmig, and C. Rohde, “Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems,” Comput. Geosci., vol. 19, pp. 299–309, 2015, doi: 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 = apr, 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. C. Rohde and C. Zeiler, “A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension,” Appl. Numer. Math., vol. 95, pp. 267--279, 2015, doi: 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. F. Kissling and C. Rohde, “The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case,” Multiscale Model. Simul., vol. 13 no. 4, pp. 1507–1541, 2015, doi: 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. J. Neusser, C. Rohde, and V. Schleper, “Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase flow with phase transition,” J. Numer. Meth. Fluids, vol. 79, no. 12, Art. no. 12, 2015, doi: 10.1002/fld.4065.
  - BibTeX
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  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 = {December}, 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
2014
1. R. Bürger, I. Kröker, and C. Rohde, “A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit,” ZAMM Z. Angew. Math. Mech., vol. 94, no. 10, Art. no. 10, 2014, doi: 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. W. Ehlers, R. Helmig, and C. Rohde, “Editorial: Deformation and transport phenomena in porous media,” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 94, no. 7–8, Art. no. 7–8, 2014, doi: 10.1002/zamm.201400559.
  - BibTeX
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  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 für 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. C. Chalons, P. Engel, and C. Rohde, “A Conservative and Convergent Scheme for Undercompressive Shock Waves,” SIAM J. Numer. Anal., vol. 52, no. 1, Art. no. 1, 2014, [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=732.
  - BibTeX
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  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. P. Engel, A. Viorel, and C. Rohde, “A Low-Order Approximation for Viscous-Capillary Phase Transition Dynamics,” Port. Math., vol. 70, no. 4, Art. no. 4, 2014, [Online]. Available: http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=723.
  - BibTeX
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  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. S. Fechter, C. Zeiler, C.-D. Munz, and C. Rohde, “Simulation of compressible multi-phase flows at extreme ambient conditions using a Discontinuous-Galerkin method,” 2014.
  - 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 }
6. A. Corli, C. Rohde, and V. Schleper, “Parabolic approximations of diffusive-dispersive equations.,” J. Math. Anal. Appl., vol. 414, pp. 773–798, 2014, [Online]. Available: http://dx.doi.org/10.1016/j.jmaa.2014.01.049.
  - BibTeX
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  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. K. Eisenschmidt, P. Rauschenberger, C. Rohde, and B. Weigand, “Modelling of freezing processes in super-cooled droplets on sub-grid scale,” 2013.
  - 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 }
2. C. Rohde, W. Wang, and F. Xie, “Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation Hydrodynamics Model,” Mathematical Models and Methods in Applied Sciences, vol. 23, no. 03, Art. no. 03, 2013, doi: 10.1142/S0218202512500522.
  - BibTeX
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  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
2012
1. A. Corli and C. Rohde, “Singular limits for a parabolic-elliptic regularization of scalar conservation laws,” J. Differential Equations, vol. 253, no. 5, Art. no. 5, 2012, doi: 10.1016/j.jde.2012.05.006.
  - BibTeX
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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. P. Engel and C. Rohde, “On the Space-Time Expansion Discontinuous Galerkin Method,” in Hyperbolic Problems: Theory, Numerics and Applications, 2012, 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 }
3. F. Kissling and C. Rohde, “Numerical Simulation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method,” in Hyperbolic Problems: Theory, Numerics and Applications, 2012, 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 }
4. I. Kröker and C. Rohde, “Finite volume schemes for hyperbolic balance laws with multiplicative noise,” Appl. Numer. Math., vol. 62, no. 4, Art. no. 4, 2012, doi: 10.1016/j.apnum.2011.01.011.
  - BibTeX
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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
5. F. Kissling, R. Helmig, and C. Rohde, “Simulation of Infiltration Processes in the Unsaturated Zone Using a Multi-Scale Approach,” Vadose Zone J., vol. 11, no. 3, Art. no. 3, 2012, doi: 10.2136/vzj2011.0193.
  - BibTeX
  - Link
  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. R. Bürger, I. Kröker, and C. Rohde, “Uncertainty quantification for a clarifier-thickener model with random feed,” in Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2, vol. 4, Springer, 2011, pp. 195--203.
  - BibTeX
  - Link
  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
2010
1. F. Kissling and C. Rohde, “The Computation of Nonclassical Shock Waves with a Heterogeneous Multiscale Method,” Netw. Heterog. Media, vol. 5, no. 3, Art. no. 3, 2010, doi: 10.3934/nhm.2010.5.661.
  - BibTeX
  - Link
  BibTeX
  @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. C. Rohde, “A local and low-order Navier-Stokes-Korteweg system,” in Nonlinear partial differential equations and hyperbolic wave phenomena, vol. 526, Providence, RI: Amer. Math. Soc., 2010, pp. 315--337.
  - BibTeX
  - Link
  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. F. Kissling, P. G. LeFloch, and C. Rohde, “A Kinetic Decomposition for Singular Limits of non-local Conservation Laws,” J. Differential Equations, vol. 247, no. 12, Art. no. 12, 2009, doi: 10.1016/j.jde.2009.05.006.
  - BibTeX
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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. C. Rohde, N. Tiemann, and W.-A. Yong, “Weak and classical solutions for a model problem in radiation hydrodynamics,” in Hyperbolic problems: theory, numerics, applications, Berlin: Springer, 2008, pp. 891--899.
  - BibTeX
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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. C. Rohde and W.-A. Yong, “Dissipative entropy and global smooth solutions in radiation hydrodynamics and magnetohydrodynamics,” Math. Models Methods Appl. Sci., vol. 18, no. 12, Art. no. 12, 2008, doi: 10.1142/S0218202508003327.
  - BibTeX
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  BibTeX
  @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. A. Dressel and C. Rohde, “A finite-volume approach to liquid-vapour fluids with phase transition,” in Finite volumes for complex applications V, ISTE, London, 2008, pp. 53--68.
  - BibTeX
  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. J. Haink and C. Rohde, “Local discontinuous-Galerkin schemes for model problems in phase transition theory,” Commun. Comput. Phys., vol. 4, pp. 860–893, 2008, [Online]. Available: https://www.researchgate.net/profile/Christian_Rohde2/publication/228406932_Local_discontinuous-Galerkin_schemes_for_model_problems_in_phase_transition_theory/links/00b4952cb030e0da90000000.pdf.
  - BibTeX
  - Link
  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. A. Dressel and C. Rohde, “Global existence and uniqueness of solutions for a viscoelastic two-phase model,” Indiana Univ. Math. J., vol. 57, no. 2, Art. no. 2, 2008, doi: 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. C. Rohde and W.-A. Yong, “The nonrelativistic limit in radiation hydrodynamics. I. Weak entropy solutions for a model problem,” J. Differential Equations, vol. 234, no. 1, Art. no. 1, 2007, doi: 10.1016/j.jde.2006.11.010.
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  BibTeX
  @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. C. Merkle and C. Rohde, “The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques,” M2AN Math. Model. Numer. Anal., vol. 41, no. 6, Art. no. 6, 2007, doi: 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. C. Merkle and C. Rohde, “Computation of dynamical phase transitions in solids,” Appl. Numer. Math., vol. 56, no. 10–11, Art. no. 10–11, 2006, doi: 10.1016/j.apnum.2006.03.025.
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  @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
2. V. Jovanović and C. Rohde, “Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws,” SIAM J. Numer. Anal., vol. 43, no. 6, Art. no. 6, 2006, doi: 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. C. Rohde, “Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms,” SIAM J. Math. Anal., vol. 37, no. 1, Art. no. 1, 2005, doi: 10.1137/S0036141004443300.
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  BibTeX
  @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. F. Coquel, D. Diehl, C. Merkle, and C. Rohde, “Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows,” in Numerical methods for hyperbolic and kinetic problems, vol. 7, Eur. Math. Soc., Zürich, 2005, pp. 239--270.
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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. V. Jovanović and C. Rohde, “Finite-volume schemes for Friedrichs systems in multiple space dimensions: a priori and a posteriori error estimates,” Numer. Methods Partial Differential Equations, vol. 21, no. 1, Art. no. 1, 2005, doi: 10.1002/num.20026.
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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
4. C. Rohde, “Phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy,” Interfaces Free Bound., vol. 7, no. 1, Art. no. 1, 2005, doi: 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
5. M. J. Gander and C. Rohde, “Nonlinear advection problems and overlapping Schwarz waveform relaxation,” in Domain decomposition methods in science and engineering, vol. 40, Berlin: Springer, 2005, pp. 251--258.
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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
2004
1. A. Dedner and C. Rohde, “Numerical approximation of entropy solutions for hyperbolic integro-differential equations,” Numer. Math., vol. 97, no. 3, Art. no. 3, 2004, doi: 10.1007/s00211-003-0502-9.
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  @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
2. C. Rohde and M. D. Thanh, “Global existence for phase transition problems via a variational scheme,” J. Hyperbolic Differ. Equ., vol. 1, no. 4, Art. no. 4, 2004, doi: 10.1142/S0219891604000329.
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  @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. D. Kröner, M. Küther, M. Ohlberger, and C. Rohde, “A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws,” in Trends in nonlinear analysis, Berlin: Springer, 2003, pp. 289--306.
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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. A. Dedner, D. Kröner, C. Rohde, T. Schnitzer, and M. Wesenberg, “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, Berlin: Springer, 2003, pp. 573--589.
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  @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. H. Freistühler and C. Rohde, “The bifurcation analysis of the MHD Rankine-Hugoniot equations for a perfect gas,” Phys. D, vol. 185, no. 2, Art. no. 2, 2003, doi: 10.1016/S0167-2789(03)00206-9.
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  @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
4. A. Dedner, C. Rohde, and M. Wesenberg, “A new approach to divergence cleaning in magnetohydrodynamic simulations,” in Hyperbolic problems: theory, numerics, applications, Berlin: Springer, 2003, pp. 509--518.
  - 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. A. Dedner and C. Rohde, “FV-schemes for a scalar model problem of radiation magnetohydrodynamics,” in Finite volumes for complex applications, III (Porquerolles, 2002), Hermes Sci. Publ., Paris, 2002, pp. 165--172.
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  @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. M. Ohlberger and C. Rohde, “Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems,” IMA J. Numer. Anal., vol. 22, no. 2, Art. no. 2, 2002, doi: 10.1093/imanum/22.2.253.
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  @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
3. P. G. Lefloch, J. M. Mercier, and C. Rohde, “Fully discrete, entropy conservative schemes of arbitrary order,” SIAM J. Numer. Anal., vol. 40, no. 5, Art. no. 5, 2002, doi: 10.1137/S003614290240069X.
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  @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. B. Haasdonk, D. Kröner, and C. Rohde, “Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids,” Numer. Math., vol. 88, no. 3, Art. no. 3, 2001, doi: 10.1007/s211-001-8011-x.
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  @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. H. Freistühler, C. Fries, and C. Rohde, “Existence, bifurcation, and stability of profiles for classical and non-classical shock waves,” in Ergodic theory, analysis, and efficient simulation of dynamical systems, Berlin: Springer, 2001, pp. 287--309, 814.
  - BibTeX
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  @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. A. Dedner, D. Kröner, C. Rohde, and M. Wesenberg, “Godunov-type schemes for the MHD equations,” in Godunov methods (Oxford, 1999), Kluwer/Plenum, New York, 2001, pp. 209--216.
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  @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. H. Freistühler and C. Rohde, “A numerical study on viscous profiles of MHD shock waves,” in Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000), vol. 141, Basel: Birkhäuser, 2001, pp. 399--408.
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  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. P. G. LeFloch and C. Rohde, “Zero diffusion-dispersion limits for self-similar Riemann solutions to hyperbolic systems of conservation laws,” Indiana Univ. Math. J., vol. 50, no. 4, Art. no. 4, 2001, doi: 10.1512/iumj.2001.50.2057.
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  @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. T. Hillen, C. Rohde, and F. Lutscher, “Existence of weak solutions for a hyperbolic model of chemosensitive movement,” J. Math. Anal. Appl., vol. 260, no. 1, Art. no. 1, 2001, doi: 10.1006/jmaa.2001.7447.
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  @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. B. Haasdonk, D. Kröner, and C. Rohde, “Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids,” Numer. Math., vol. 88, no. 3, Art. no. 3, 2001, doi: 10.1007/s211-001-8011-x.
  - BibTeX
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  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. A. Dedner, D. Kröner, C. Rohde, and M. Wesenberg, “MHD instabilities arising in solar physics: a numerical approach,” in Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000), vol. 141, Basel: Birkhäuser, 2001, pp. 277--286.
  - 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. P. G. Lefloch and C. Rohde, “High-order schemes, entropy inequalities, and nonclassical shocks,” SIAM J. Numer. Anal., vol. 37, no. 6, Art. no. 6, 2000, doi: 10.1137/S0036142998345256.
  - BibTeX
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  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. A. Dedner, C. Rohde, and M. Wesenberg, “A MHD-simulation in solar physics,” in Finite volumes for complex applications II, Hermes Sci. Publ., Paris, 1999, pp. 491--498.
  - 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. H. Freistühler and C. Rohde, “Numerical methods for viscous profiles of non-classical shock waves,” in Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich, 1998), vol. 129, Basel: Birkhäuser, 1999, pp. 333--342.
  - 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. C. Rohde, “Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2D,” Numer. Math., vol. 81, no. 1, Art. no. 1, 1998, doi: 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. C. Rohde, “Entropy solutions for weakly coupled hyperbolic systems in several space dimensions,” Z. Angew. Math. Phys., vol. 49, no. 3, Art. no. 3, 1998, doi: 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 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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