This image shows Christian Rohde

Christian Rohde

Prof. Dr.

Head of Group
Institute of Applied Analysis and Numerical Simulation
Chair of Applied Mathematics
[Photo: Laura Holzmann Photography]

Contact

+49 711 685 65524
 +49 711 685 65599

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.131

Office Hours

Fridays 1 - 2 pm and by appointment

  1. 2025

    1. Rohde, C., Wendt, F.: Mathematical Justification of a Baer-Nunziato Model for a Compressible Viscous Fluid with Phase Transition, https://arxiv.org/abs/2504.10161, (2025).
    2. Schwarz, A., Keim, J., Rohde, C., Beck, A.: Entropy stable shock capturing for high-order DGSEM on moving meshes, https://arxiv.org/abs/2503.23237, (2025).
    3. Huang, Q., Rohde, C., Yong, W.-A., Zhang, R.: A hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility. J. Differential Equations. 438, 113339 (2025). https://doi.org/10.1016/j.jde.2025.113339.
    4. Schwarz, A., Kempf, D., Keim, J., Kopper, P., Rohde, C., Beck, A.: Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows, https://arxiv.org/abs/2504.00173, (2025).
    5. Barthwal, R., Rohde, C.: A hyperbolic model for two-layer thin film flow with a perfectly soluble anti-surfactant, https://arxiv.org/abs/2502.17205, (2025).
    6. Duvenbeck, L., Riethmüller, C., Rohde, C.: Data-driven geometric parameter optimization for PD-GMRES, (2025). https://doi.org/https://doi.org/10.48550/arXiv.2503.09728.
    7. Ghosh, T., Bringedal, C., Rohde, C., Helmig, R.: A phase-field approach to model evaporation from porous media: Modeling and upscaling. Advances in Water Resources. 104922 (2025). https://doi.org/https://doi.org/10.1016/j.advwatres.2025.104922.
    8. Schollenberger, T., Rohde, C., Helmig, R.: Two-phase pore-network model for evaporation-driven salt precipitation -- representation and analysis of pore-scale processes, https://arxiv.org/abs/2503.22533, (2025).

  2. 2024

    1. Miao, Y., Rohde, C., Tang, H.: Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities. Stoch. Partial Differ. Equ. Anal. Comput. 12, 614–674 (2024). https://doi.org/10.1007/s40072-023-00291-z.
    2. Mel’nyk, T., Rohde, C.: Asymptotic expansion for convection-dominated transport in a thin graph-like junction. Analysis and Applications. 22 (05), 833–879 (2024). https://doi.org/https://doi.org/10.1142/S0219530524500040.
    3. Schollenberger, T., von Wolff, L., Bringedal, C., Pop, I.S., Rohde, C., Helmig, R.: Investigation of Different Throat Concepts for Precipitation Processes in Saturated Pore-Network Models. Transport in Porous Media. (2024). https://doi.org/10.1007/s11242-024-02125-5.
    4. Magiera, J., Rohde, C.: A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate. Communications on Applied Mathematics and Computation. (2024). https://doi.org/10.1007/s42967-023-00349-8.
    5. Keim, J., Konan, H.-C., Rohde, C.: A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow, https://arxiv.org/abs/2412.11904, (2024).
    6. Mel’nyk, T., Rohde, C.: Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks. J. Math. Anal. Appl. 529, Paper No. 127587, 35 (2024). https://doi.org/10.1016/j.jmaa.2023.127587.
    7. Alkämper, M., Magiera, J., Rohde, C.: An Interface-Preserving Moving Mesh in Multiple Space Dimensions. ACM Trans. Math. Softw. 50, (2024). https://doi.org/10.1145/3630000.
    8. Hörl, M., Rohde, C.: Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture. Netw. Heterog. Media. 19, 114–156 (2024). https://doi.org/10.3934/nhm.2024006.
    9. Mel’nyk, T., Rohde, C.: Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains. Nonlinear Differ. Equ. Appl. 31:105, (2024). https://doi.org/https://doi.org/10.1007/s00030-024-00997-6.
    10. Lukácová-Medvid’ová, M., Rohde, C.: Mathematical Challenges for the Theory of Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness. Jahresber. Dtsch. Math.-Ver. 126, 283–311 (2024). https://doi.org/10.1365/s13291-024-00290-6.
    11. Mel’nyk, T., Rohde, C.: Muskat-Leverett two-phase flow in thin cylindric porous media: Asymptotic approach, https://arxiv.org/abs/2411.02923, (2024).
    12. Mel’nyk, T., Rohde, C.: Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: strong boundary interactions. Asymptotic Analysis. 137, 27–52 (2024). https://doi.org/10.3233/ASY-231876.

  3. 2023

    1. Burbulla, S., Hörl, M., Rohde, C.: Flow in Porous Media with Fractures of Varying Aperture. SIAM J. Sci. Comput. 45, A1519–A1544 (2023). https://doi.org/10.1137/22M1510406.
    2. Keim, J., Munz, C.-D., Rohde, C.: A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in Confined Domains. J. Comput. Phys. 474, 111830 (2023). https://doi.org/https://doi.org/10.1016/j.jcp.2022.111830.
    3. Seus, D., Radu, F.A., Rohde, C.: Towards hybrid two-phase modelling using linear domain decomposition. Numer. Methods Partial Differential Equations. 39, 622–656 (2023). https://doi.org/https://doi.org/10.1002/num.22906.
    4. Keim, J., Schwarz, A., Chiocchetti, S., Rohde, C., Beck, A.: A Reinforcement Learning Based Slope Limiter for Two-Dimensional Finite Volume Schemes. (2023). https://doi.org/10.13140/RG.2.2.18046.87363.
    5. Burbulla, S., Formaggia, L., Rohde, C., Scotti, A.: Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models. Comput. Methods Appl. Mech. Engrg. 403, (2023). https://doi.org/https://doi.org/10.1016/j.cma.2022.115699.
    6. Gander, M.J., Lunowa, S.B., Rohde, C.: Consistent and Asymptotic-Preserving Finite-Volume Robin Transmission Conditions for Singularly Perturbed Elliptic Equations. In: Brenner, S.C., Chung, E., Klawonn, A., Kwok, F., Xu, J., and Zou, J. (eds.) Domain Decomposition Methods in Science and Engineering XXVI. pp. 443–450. Springer International Publishing, Cham (2023).
    7. Gander, M.J., Lunowa, S.B., Rohde, C.: Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations. SIAM J. Sci. Comput. 45, A49–A73 (2023). https://doi.org/10.1137/21M1415005.

  4. 2022

    1. Burbulla, S., Dedner, A., Hörl, M., Rohde, C.: Dune-MMesh: The Dune Grid Module for Moving Interfaces. J. Open Source Softw. 7, 3959 (2022). https://doi.org/10.21105/joss.03959.
    2. Magiera, J., Rohde, C.: Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics. In: Schulte, K., Tropea, C., and Weigand, B. (eds.) Droplet Dynamics under Extreme Ambient Conditions. Springer International Publishing (2022). https://doi.org/10.1007/978-3-031-09008-0_4.
    3. Burbulla, S., Rohde, C.: A finite-volume moving-mesh method for two-phase flow in fracturing porous media. J. Comput. Phys. 111031 (2022). https://doi.org/https://doi.org/10.1016/j.jcp.2022.111031.
    4. Massa, F., Ostrowski, L., Bassi, F., Rohde, C.: An artificial Equation of State based Riemann solver for a discontinuous Galerkin discretization of the incompressible Navier–Stokes equations. J. Comput. Phys. 110705 (2022). https://doi.org/https://doi.org/10.1016/j.jcp.2021.110705.
    5. Magiera, J., Rohde, C.: A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces. J. Comput. Phys. 111551 (2022). https://doi.org/https://doi.org/10.1016/j.jcp.2022.111551.

  5. 2021

    1. Alonso-Orán, D., Rohde, C., Tang, H.: A local-in-time theory for singular SDEs with applications to fluid models with transport noise. J. Nonlinear Sci. 31, Paper No. 98, 55 (2021). https://doi.org/doi.org/10.1007/s00332-021-09755-9.
    2. Rohde, C., Von Wolff, L.: A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution. Mathematical Models and Methods in Applied Sciences. 31, 1–35 (2021). https://doi.org/10.1142/S0218202521500019.
    3. Dürrwächter, J., Meyer, F., Kuhn, T., Beck, A., Munz, C.-D., Rohde, C.: A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations. Computers & Fluids. 228, 1850044, 20 (2021). https://doi.org/10.1016/j.compfluid.2021.105039.
    4. Giesselmann, J., Meyer, F., Rohde, C.: Error control for statistical solutions of hyperbolic systems of conservation laws. Calcolo. 58, Paper No. 23, 29 (2021). https://doi.org/10.1007/s10092-021-00417-6.
    5. von Wolff, L., Weinhardt, F., Class, H., Hommel, J., Rohde, C.: Investigation of Crystal Growth in Enzymatically Induced Calcite Precipitation by Micro-Fluidic Experimental Methods and Comparison with Mathematical Modeling. Transp. Porous Media. 137, 327–343 (2021). https://doi.org/10.1007/s11242-021-01560-y.
    6. Rohde, C., Tang, H.: On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena. NoDEA Nonlinear Differential Equations Appl. 28, Paper No. 5, 34 (2021). https://doi.org/10.1007/s00030-020-00661-9.
    7. Beck, A., Dürrwächter, J., Kuhn, T., Meyer, F., Munz, C.-D., Rohde, C.: Uncertainty Quantification in High Performance Computational Fluid Dynamics. In: Nagel, W.E., Kröner, D.H., and Resch, M.M. (eds.) High Performance Computing in Science and Engineering ’19. pp. 355–371. Springer International Publishing, Cham (2021).
    8. Gander, M., Lunowa, S., Rohde, C.: Consistent and asymptotic-preserving finite-volume domain decomposition methods for singularly perturbed elliptic equations. In: Domain Decomposition Methods in Science and Engineering XXVI. Lect. Notes Comput. Sci. Eng., Springer, Cham (2021).
    9. Rohde, C., Tang, H.: On a stochastic Camassa-Holm type equation with higher order nonlinearities. J. Dynam. Differential Equations. 33, 1823–1852 (2021). https://doi.org/https://doi.org/10.1007/s10884-020-09872-1.

  6. 2020

    1. Giesselmann, J., Meyer, F., Rohde, C.: An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws. In: Bressan, A., Lewicka, M., Wang, D., and Zheng, Y. (eds.) Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018. pp. 449–456. AIMS Series on Applied Mathematics (2020).
    2. Burbulla, S., Rohde, C.: A fully conforming finite volume approach to two-phase flow in fractured porous media. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., and Fuhrmann, J. (eds.) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. pp. 547–555. Springer International Publishing, Cham (2020). https://doi.org/https://doi.org/10.1007/978-3-030-43651-3_51.
    3. Armiti-Juber, A., Rohde, C.: On the well-posedness of a nonlinear fourth-order extension of Richards’ equation. J. Math. Anal. Appl. 487, 124005 (2020). https://doi.org/https://doi.org/10.1016/j.jmaa.2020.124005.
    4. Giesselmann, J., Meyer, F., Rohde, C.: A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws. BIT Numerical Mathematics. 60, 619–649 (2020). https://doi.org/10.1007/s10543-019-00794-z.
    5. Magiera, J., Ray, D., Hesthaven, J.S., Rohde, C.: Constraint-aware neural networks for Riemann problems. J. Comput. Phys. 409, (2020). https://doi.org/https://doi.org/10.1016/j.jcp.2020.109345.
    6. Beck, A., Dürrwächter, J., Kuhn, T., Meyer, F., Munz, C.-D., Rohde, C.: $hp$-Multilevel Monte Carlo methods for uncertainty quantification of compressible flows. SIAM J. Sci. Comput. 42, B1067–B1091 (2020). https://doi.org/https://doi.org/10.1137/18M1210575.
    7. Hitz, T., Keim, J., Munz, C.-D., Rohde, C.: A parabolic relaxation model for the Navier-Stokes-Korteweg equations. J. Comput. Phys. 421, 109714 (2020). https://doi.org/https://doi.org/10.1016/j.jcp.2020.109714.
    8. Rohde, C., von Wolff, L.: Homogenization of non-local Navier-Stokes-Korteweg equations for compressible liquid-vapour flow in porous media. SIAM J. Math. Anal. 52, 6155–6179 (2020). https://doi.org/10.1137/19M1242434.
    9. Giesselmann, J., Meyer, F., Rohde, C.: A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method. IMA J. Numer. Anal. 40, 1094–1121 (2020). https://doi.org/10.1093/imanum/drz004.
    10. Ostrowski, L., Rohde, C.: Compressible multi-component flow in porous media with Maxwell-Stefan diffusion. Math. Meth. Appl. Sci. 1–22 (2020).
    11. Ostrowski, L., Rohde, C.: Phase field modelling for compressible droplet impingement. In: Bressan, A., Lewicka, M., Wang, D., and Zheng, Y. (eds.) Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Seventeenth International Conference on Hyperbolic Problems 2018. pp. 586–593. AIMS Series on Applied Mathematics (2020).
    12. Ostrowski, L., Massa, F.C., Rohde, C.: A phase field approach to compressible droplet impingement. In: Lamanna, G., Tonini, S., Cossali, G.E., and Weigand, B. (eds.) Droplet Interactions and Spray Processes. pp. 113–126. Springer International Publishing, Cham (2020).

  7. 2019

    1. Sharanya, V., Sekhar, G.P.R., Rohde, C.: Surfactant-induced migration of a spherical droplet in non-isothermal Stokes flow. Physics of Fluids. 31, 12110 (2019). https://doi.org/10.1063/1.5064694.
    2. Colombo, R.M., LeFloch, P.G., Rohde, C., Trivisa, K.: Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics. Oberwohlfach Rep. 1419–1497 (2019).
    3. Seus, D., Radu, F.A., Rohde, C.: A linear domain decomposition method for two-phase flow in porous media. Numerical Mathematics and Advanced Applications ENUMATH 2017. 603–614 (2019). https://doi.org/https://doi.org/10.1007/978-3-319-96415-7_55.
    4. Kuhn, T., Dürrwächter, J., Meyer, F., Beck, A., Rohde, C., Munz, C.-D.: Uncertainty quantification for direct aeroacoustic simulations of cavity flows. J. Theor. Comput. Acoust. 27, 1850044, 20 (2019). https://doi.org/https://doi.org/10.1142/S2591728518500445.
    5. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Santin, G., Wittwar, D., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., Rohde, C.: Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario. Comput. Geosci. 2, 339–354 (2019). https://doi.org/https://doi.org/10.1007/s10596-018-9785-x.
    6. Armiti-Juber, A., Rohde, C.: Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media. J. Math. Anal. Appl. 477, 592–612 (2019). https://doi.org/https://doi.org/10.1016/j.jmaa.2019.04.049.
    7. Armiti-Juber, A., Rohde, C.: On Darcy-and Brinkman-type models for two-phase flow in asymptotically flat domains. Comput. Geosci. 23, 285–303 (2019). https://doi.org/https://doi.org/10.1007/s10596-018-9756-2.

  8. 2018

    1. Fechter, S., Munz, C.-D., Rohde, C., Zeiler, C.: Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension. Comput. & Fluids. 169, 169–185 (2018). https://doi.org/http://dx.doi.org/10.1016/j.compfluid.2017.03.026.
    2. Rohde, C.: Fully resolved compressible two-phase flow : modelling, analytical and numerical issues. In: Bulicek, M., Feireisl, E., and Pokorný, M. (eds.) New trends and results in mathematical description of fluid flows. pp. 115–181. Birkhäuser, Basel (2018). https://doi.org/10.1007/978-3-319-94343-5.
    3. Magiera, J., Rohde, C.: A particle-based multiscale solver for compressible liquid-vapor flow. Springer Proc. Math. Stat. 291–304 (2018). https://doi.org/10.1007/978-3-319-91548-7_23.
    4. Sharanya, V., Sekhar, G.P.R., Rohde, C.: 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. 82–103 (2018). https://doi.org/https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.008.
    5. Chalons, C., Magiera, J., Rohde, C., Wiebe, M.: A finite-volume tracking scheme for two-phase compressible flow. Springer Proc. Math. Stat. 309–322 (2018). https://doi.org/https://doi.org/10.1007/978-3-319-91545-6_25.
    6. Rohde, C., Zeiler, C.: On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension. Z. Angew. Math. Phys. 69, Art. 76 (2018). https://doi.org/https://doi.org/10.1007/s00033-018-0958-1.
    7. Raja Sekhar, G.P., Sharanya, V., Rohde, C.: Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number. International Journal of Multiphase Flow. 107, 82–103 (2018).
    8. Seus, D., Pop, I.S., Rohde, C., Mitra, K., Radu, F.: A linear domain decompostition method for partially saturated flow in porous media. Comput. Methods Appl. Mech. Eng. 333, 331–355 (2018). https://doi.org/https://doi.org/10.1016/j.cma.2018.01.029.
    9. Seus, D., Mitra, K., Pop, I.S., Radu, F.A., Rohde, C.: A linear domain decomposition method for partially saturated flow in porous media. Comp. Methods Appl. Mech. Eng. 333, 331–355 (2018). https://doi.org/https://doi.org/10.1016/j.cma.2018.01.029.

  9. 2017

    1. Köppel, M., Kröker, I., Rohde, C.: Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems Governing Two-Phase Flow in Heterogeneous Porous Media. Comput. Geosci. 21, 807–832 (2017). https://doi.org/10.1007/s10596-017-9662-z.
    2. Fechter, S., Munz, C.-D., Rohde, C., Zeiler, C.: A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension. J. Comput. Phys. 336, 347–374 (2017). https://doi.org/10.1016/j.jcp.2017.02.001.
    3. Kutter, M., Rohde, C., Sändig, A.-M.: Well-posedness of a two scale model for liquid phase epitaxy with elasticity. Contin. Mech. Thermodyn. 29, 989–1016 (2017). https://doi.org/10.1007/s00161-015-0462-1.
    4. Chalons, C., Rohde, C., Wiebe, M.: A finite volume method for undercompressive shock waves in two space dimensions. ESAIM Math. Model. Numer. Anal. 51, 1987–2015 (2017). https://doi.org/https://doi.org/10.1051/m2an/2017027.
    5. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Wittwar, D., Santin, G., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., Rohde, C.: Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage, https://doi.org/10.5281/zenodo.933827, (2017). https://doi.org/10.5281/zenodo.933827.
    6. Köppel, M., Franzelin, F., Kröker, I., Oladyshkin, S., Santin, G., Wittwar, D., Barth, A., Haasdonk, B., Nowak, W., Pflüger, D., Rohde, C.: Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario. University of Stuttgart (2017).

  10. 2016

    1. Betancourt, F., Rohde, C.: Finite-Volume Schemes for Friedrichs Systems with Involutions. App. Math. Comput. 272, Part 2, 420–439 (2016). https://doi.org/10.1016/j.amc.2015.03.050.
    2. Redeker, M., Pop, I.S., Rohde, C.: Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous Media. IMA J. Appl. Math. 81(5), 898–939 (2016). https://doi.org/https://doi.org/10.1093/imamat/hxw023.
    3. Colombo, R.M., LeFloch, P.G., Rohde, C.: Hyperbolic techniques in Modelling, Analysis and Numerics. Oberwolfach Reports. 13, 1683–1751 (2016). https://doi.org/10.4171/OWR/2016/30.
    4. Dragomirescu, F.I., Eisenschmidt, K., Rohde, C., Weigand, B.: Perturbation solutions for the finite radially symmetric Stefan problem. INTERNATIONAL JOURNAL OF THERMAL SCIENCES. 104, 386–395 (2016). https://doi.org/10.1016/j.ijthermalsci.2016.01.019.
    5. Diehl, D., Kremser, J., Kröner, D., Rohde, C.: Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions. Appl. Math. Comput. 272, 309–335 (2016). https://doi.org/10.1016/j.amc.2015.09.080.
    6. Magiera, J., Rohde, C., Rybak, I.: A hyperbolic-elliptic model problem for coupled surface-subsurface flow. Transp. Porous Media. 114, 425–455 (2016). https://doi.org/10.1007/S11242-015-0548-Z.
    7. Dragomirescu, I., Eisenschmidt, K., Rohde, C., Weigand, B.: Perturbation solutions for the finite radially symmetric Stefan problem. Inter. J. Thermal Sci. 104, 386–395 (2016). https://doi.org/https://doi.org/10.1016/j.ijthermalsci.2016.01.019.
    8. Dumbser, M., Gassner, G., Rohde, C., Roller, S.: Preface to the special issue ``Recent Advances in Numerical Methods for Hyperbolic Partial Differential Equations″. APPLIED MATHEMATICS AND COMPUTATION. 272, 235–236 (2016). https://doi.org/10.1016/j.amc.2015.11.023.
    9. Barth, A., Bürger, R., Kröker, I., Rohde, C.: Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach. Computers & Chemical Engineering. 89, 11–26 (2016). https://doi.org/http://dx.doi.org/10.1016/j.compchemeng.2016.02.016.
    10. Sharanya, V., Sekhar, G.P.R., Rohde, C.: Bed of polydisperse viscous spherical drops under thermocapillary effects. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. 67, (2016). https://doi.org/10.1007/s00033-016-0699-y.
    11. Köppel, M., Rohde, C.: Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media. PAMM Proc. Appl. Math. Mech. 16, 749–750 (2016). https://doi.org/10.1002/pamm.201610363.
    12. Kabil, B., Rohde, C.: Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension. Math. Meth. Appl. Sci. 39, 5409–5426 (2016). https://doi.org/10.1002/mma.3926.
    13. Diehl, D., Kremser, J., Kröner, D., Rohde, C.: Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions. Appl. Math. Comput. 272, 309–335 (2016). https://doi.org/10.1016/j.amc.2015.09.080.

  11. 2015

    1. Neusser, J., Rohde, C., Schleper, V.: Relaxation of the Navier-Stokes-Korteweg Equations for Compressible Two-Phase Flow with Phase Transition. J. Numer. Methods Fluids. 79, 615–639 (2015). https://doi.org/10.1002/fld.4065.
    2. Rybak, I., Magiera, J., Helmig, R., Rohde, C.: Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems. Comput. Geosci. 19, 299–309 (2015). https://doi.org/10.1007/s10596-015-9469-8.
    3. Rohde, C., Zeiler, C.: A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension. APPLIED NUMERICAL MATHEMATICS. 95, 267–279 (2015). https://doi.org/10.1016/j.apnum.2014.05.001.
    4. Kröker, I., Nowak, W., Rohde, C.: A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems. Comput. Geosci. 19, 269–284 (2015). https://doi.org/10.1007/s10596-014-9464-5.
    5. Neusser, J., Rohde, C., Schleper, V.: Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase flow with phase transition. J. Numer. Meth. Fluids. 79, 615–639 (2015). https://doi.org/10.1002/fld.4065.
    6. Kissling, F., Rohde, C.: The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case. Multiscale Model. Simul. 13 no. 4, 1507–1541 (2015). https://doi.org/10.1137/120899236.
    7. Kroeker, I., Nowak, W., Rohde, C.: A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems. COMPUTATIONAL GEOSCIENCES. 19, 269–284 (2015). https://doi.org/10.1007/s10596-014-9464-5.

  12. 2014

    1. Ehlers, W., Helmig, R., Rohde, C.: Editorial: Deformation and transport phenomena in porous media. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 94, 559 (2014). https://doi.org/10.1002/zamm.201400559.
    2. Bürger, R., Kröker, I., Rohde, C.: A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit. ZAMM Z. Angew. Math. Mech. 94, 793–817 (2014). https://doi.org/10.1002/zamm.201200174.
    3. Chalons, C., Engel, P., Rohde, C.: A Conservative and Convergent Scheme for Undercompressive Shock Waves. SIAM J. Numer. Anal. 52, 554–579 (2014).
    4. Köppel, M., Kröker, I., Rohde, C.: Stochastic Modeling for Heterogeneous Two-Phase Flow. In: Fuhrmann, J., Ohlberger, M., and Rohde, C. (eds.) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. pp. 353–361. Springer International Publishing (2014). https://doi.org/10.1007/978-3-319-05684-5_34.
    5. Kabil, B., Rohde, C.: The influence of surface tension and configurational forces on the stability of liquid-vapor interfaces. Nonlinear Analysis: Theory, Methods & Applications. 107, 63–75 (2014).
    6. Armiti-Juber, A., Rohde, C.: Almost Parallel Flows in Porous Media. In: Fuhrmann, J., Ohlberger, M., and Rohde, C. (eds.) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. pp. 873–881. Springer International Publishing (2014). https://doi.org/10.1007/978-3-319-05591-6_88.
    7. Engel, P., Viorel, A., Rohde, C.: A Low-Order Approximation for Viscous-Capillary Phase Transition Dynamics. Port. Math. 70, 319–344 (2014).
    8. Corli, A., Rohde, C., Schleper, V.: Parabolic approximations of diffusive-dispersive equations. J. Math. Anal. Appl. 414, 773–798 (2014).
    9. Fechter, S., Zeiler, C., Munz, C.-D., Rohde, C.: Simulation of compressible multi-phase flows at extreme ambient conditions using a Discontinuous-Galerkin method. In: ILASS Europe, 26th European Conference on Liquid Atomization and Spray Systems (2014).

  13. 2013

    1. Rohde, C., Wang, W., Xie, F.: Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves. Communications on Pure and Applied Analysis. 12, 2145–2171 (2013). https://doi.org/10.3934/cpaa.2013.12.2145.
    2. Eck, Ch., Kutter, M., Sändig, A.-M., Rohde, Ch.: A two scale model for liquid phase epitaxy with elasticity: An iterative procedure. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 93, 745–761 (2013). https://doi.org/10.1002/zamm.201200238.
    3. Rohde, C., Wang, W., Xie, F.: Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation Hydrodynamics Model. Mathematical Models and Methods in Applied Sciences. 23, 441–469 (2013). https://doi.org/10.1142/S0218202512500522.
    4. Eisenschmidt, K., Rauschenberger, P., Rohde, C., Weigand, B.: Modelling of freezing processes in super-cooled droplets on sub-grid scale. In: ILASS�Europe, 25th European Conference on Liquid Atomization and Spray Systems (2013).

  14. 2012

    1. Chalons, C., Coquel, F., Engel, P., Rohde, C.: Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems. SIAM Journal on Scientific Computing. 34, A1753––A1776 (2012). https://doi.org/10.1137/110848815.
    2. Jaegle, F., Rohde, C., Zeiler, C.: A multiscale method for compressible liquid-vapor flow with surface tension. ESAIM: Proc. 38, 387–408 (2012). https://doi.org/10.1051/proc/201238022.
    3. Kissling, F., Helmig, R., Rohde, C.: Simulation of Infiltration Processes in the Unsaturated Zone Using a Multi-Scale Approach. Vadose Zone J. 11, – (2012). https://doi.org/10.2136/vzj2011.0193.
    4. Engel, P., Rohde, C.: On the Space-Time Expansion Discontinuous Galerkin Method. In: Li, T. and Jiang, S. (eds.) Hyperbolic Problems: Theory, Numerics and Applications. pp. 406–414 (2012).
    5. Kröker, I., Rohde, C.: Finite volume schemes for hyperbolic balance laws with multiplicative noise. Appl. Numer. Math. 62, 441–456 (2012). https://doi.org/10.1016/j.apnum.2011.01.011.
    6. Richter, T., Rudlof, S., Adjibadji, B., Bernlöhr, H., Gröninger, C., Munz, C.-D., Stock, A., Rohde, C., Helmig, R.: ViPLab: a virtual programming laboratory for mathematics and engineering. Interactive Technology and Smart Education. 9, 246–262 (2012). https://doi.org/10.1108/17415651211284039.
    7. Corli, A., Rohde, C.: Singular limits for a parabolic-elliptic regularization of scalar conservation laws. J. Differential Equations. 253, 1399–1421 (2012). https://doi.org/10.1016/j.jde.2012.05.006.
    8. Dreyer, W., Giesselmann, J., Kraus, C., Rohde, C.: Asymptotic Analysis for Korteweg Models. Interfaces Free Bound. 14, 105–143 (2012).
    9. Kissling, F., Rohde, C.: Numerical Simulation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method. In: Li, T. and Jiang, S. (eds.) Hyperbolic Problems: Theory, Numerics and Applications. pp. 469–478 (2012).
    10. Rohde, C., Xie, F.: Global existence and blowup phenomenon for a 1D radiation hydrodynamics model problem. Math. Methods Appl. Sci. 35, 564–573 (2012). https://doi.org/10.1002/mma.1593.

  15. 2011

    1. Richter, Th., Rudlof, S., Adjibadji, B., Berlohr, H., Gruninger, Ch., Munz, C.-D., Rohde, Ch., Helmig, R.: ViPLab - A Virtual Programming Laboratory for Mathematics and Engineering. In: Proceedings of the 2011 IEEE International Symposium on Multimedia. pp. 537–542. IEEE Computer Society, Washington, DC, USA (2011). https://doi.org/10.1109/ISM.2011.95.
    2. Bürger, R., Kröker, I., Rohde, C.: Uncertainty quantification for a clarifier-thickener model with random feed. In: Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2. pp. 195–203. Springer (2011). https://doi.org/10.1007/978-3-642-20671-9_21.

  16. 2010

    1. Kissling, F., Rohde, C.: The Computation of Nonclassical Shock Waves with a Heterogeneous Multiscale Method. Netw. Heterog. Media. 5, 661–674 (2010). https://doi.org/10.3934/nhm.2010.5.661.
    2. Rohde, C.: A local and low-order Navier-Stokes-Korteweg system. In: Nonlinear partial differential equations and hyperbolic wave phenomena. pp. 315–337. Amer. Math. Soc., Providence, RI (2010). https://doi.org/10.1090/conm/526/10387.

  17. 2009

    1. Kissling, F., LeFloch, P.G., Rohde, C.: A Kinetic Decomposition for Singular Limits of non-local Conservation Laws. J. Differential Equations. 247, 3338–3356 (2009). https://doi.org/10.1016/j.jde.2009.05.006.

  18. 2008

    1. Rohde, C., Tiemann, N., Yong, W.-A.: Weak and classical solutions for a model problem in radiation hydrodynamics. In: Hyperbolic problems: theory, numerics, applications. pp. 891–899. Springer, Berlin (2008). https://doi.org/10.1007/978-3-540-75712-2_93.
    2. Dressel, A., Rohde, C.: Global existence and uniqueness of solutions for a viscoelastic two-phase model. Indiana Univ. Math. J. 57, 717–755 (2008). https://doi.org/10.1512/iumj.2008.57.3271.
    3. Dressel, A., Rohde, C.: A finite-volume approach to liquid-vapour fluids with phase transition. In: Finite volumes for complex applications V. pp. 53–68. ISTE, London (2008).
    4. Rohde, C., Yong, W.-A.: Dissipative entropy and global smooth solutions in radiation hydrodynamics and magnetohydrodynamics. Math. Models Methods Appl. Sci. 18, 2151–2174 (2008). https://doi.org/10.1142/S0218202508003327.
    5. Haink, J., Rohde, C.: Local discontinuous-Galerkin schemes for model problems in phase transition theory. Commun. Comput. Phys. 4, 860–893 (2008).

  19. 2007

    1. Rohde, C., Yong, W.-A.: The nonrelativistic limit in radiation hydrodynamics. I. Weak entropy solutions for a model problem. J. Differential Equations. 234, 91–109 (2007). https://doi.org/10.1016/j.jde.2006.11.010.
    2. Merkle, C., Rohde, C.: The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques. M2AN Math. Model. Numer. Anal. 41, 1089–1123 (2007). https://doi.org/10.1051/m2an:2007048.

  20. 2006

    1. Haink, J., Rohde, C.: Phase transition in compressible media and nonlocal capillarity terms. In: Hyperbolic problems: theory, numerics and applications. I. pp. 147–154. Yokohama Publ., Yokohama (2006).
    2. Jovanović, V., Rohde, C.: Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws. SIAM J. Numer. Anal. 43, 2423––2449 (electronic) (2006). https://doi.org/10.1137/S0036142903438136.
    3. Diehl, D., Rohde, C.: On the structure of MHD shock waves in diffusive-dispersive media. J. Math. Fluid Mech. 8, 120–145 (2006). https://doi.org/10.1007/s00021-004-0149-z.
    4. Merkle, C., Rohde, C.: Computation of dynamical phase transitions in solids. Appl. Numer. Math. 56, 1450–1463 (2006). https://doi.org/10.1016/j.apnum.2006.03.025.

  21. 2005

    1. Coquel, F., Diehl, D., Merkle, C., Rohde, C.: Sharp and diffuse interface methods for phase transition problems in liquid-vapour flows. In: Numerical methods for hyperbolic and kinetic problems. pp. 239–270. Eur. Math. Soc., Zürich (2005). https://doi.org/10.4171/012-1/11.
    2. Gander, M.J., Rohde, C.: Nonlinear advection problems and overlapping Schwarz waveform relaxation. In: Domain decomposition methods in science and engineering. pp. 251–258. Springer, Berlin (2005). https://doi.org/10.1007/3-540-26825-1_23.
    3. Rohde, C.: Scalar conservation laws with mixed local and nonlocal diffusion-dispersion terms. SIAM J. Math. Anal. 37, 103––129 (electronic) (2005). https://doi.org/10.1137/S0036141004443300.
    4. Rohde, C.: On local and non-local Navier-Stokes-Korteweg systems for liquid-vapour phase transitions. ZAMM Z. Angew. Math. Mech. 85, 839–857 (2005). https://doi.org/10.1002/zamm.200410211.
    5. Rohde, C.: Phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy. Interfaces Free Bound. 7, 107–129 (2005). https://doi.org/10.4171/IFB/116.
    6. Dedner, A., Kröner, D., Rohde, C., Wesenberg, M.: Radiation magnetohydrodynamics: analysis for model problems and efficient 3d-simulations for the full system. In: Analysis and numerics for conservation laws. pp. 163–202. Springer, Berlin (2005). https://doi.org/10.1007/3-540-27907-5_8.
    7. Jovanović, V., Rohde, C.: Finite-volume schemes for Friedrichs systems in multiple space dimensions: a priori and a posteriori error estimates. Numer. Methods Partial Differential Equations. 21, 104–131 (2005). https://doi.org/10.1002/num.20026.
    8. Gander, M.J., Rohde, C.: Overlapping Schwarz waveform relaxation for convection-dominated nonlinear conservation laws. SIAM J. Sci. Comput. 27, 415–439 (2005). https://doi.org/10.1137/030601090.

  22. 2004

    1. Dedner, A., Rohde, C., Schupp, B., Wesenberg, M.: A parallel, load-balanced MHD code on locally-adapted unstructured grids in 3d. Comput. Vis. Sci. 7, 79–96 (2004). https://doi.org/10.1007/s00791-004-0140-5.
    2. Dedner, A., Rohde, C.: Numerical approximation of entropy solutions for hyperbolic integro-differential equations. Numer. Math. 97, 441–471 (2004). https://doi.org/10.1007/s00211-003-0502-9.
    3. Rohde, C., Thanh, M.D.: Global existence for phase transition problems via a variational scheme. J. Hyperbolic Differ. Equ. 1, 747–768 (2004). https://doi.org/10.1142/S0219891604000329.

  23. 2003

    1. Dedner, A., Rohde, C., Wesenberg, M.: Efficient higher-order finite volume schemes for (real gas) magnetohydrodynamics. In: Hyperbolic problems: theory, numerics, applications. pp. 499–508. Springer, Berlin (2003).
    2. Dedner, A., Rohde, C., Wesenberg, M.: A new approach to divergence cleaning in magnetohydrodynamic simulations. In: Hyperbolic problems: theory, numerics, applications. pp. 509–518. Springer, Berlin (2003).
    3. Kröner, D., Küther, M., Ohlberger, M., Rohde, C.: A posteriori error estimates and adaptive methods for hyperbolic and convection dominated parabolic conservation laws. In: Trends in nonlinear analysis. pp. 289–306. Springer, Berlin (2003).
    4. Dedner, A., Kröner, D., Rohde, C., Schnitzer, T., Wesenberg, M.: Comparison of finite volume and discontinuous Galerkin methods of higher order for systems of conservation laws in multiple space dimensions. In: Geometric analysis and nonlinear partial differential equations. pp. 573–589. Springer, Berlin (2003).
    5. Rohde, C., Zajaczkowski, W.: On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation. Appl. Math. 48, 257–277 (2003). https://doi.org/10.1023/A:1026010631074.
    6. Freistühler, H., Rohde, C.: The bifurcation analysis of the MHD Rankine-Hugoniot equations for a perfect gas. Phys. D. 185, 78–96 (2003). https://doi.org/10.1016/S0167-2789(03)00206-9.

  24. 2002

    1. Dedner, A., Rohde, C.: FV-schemes for a scalar model problem of radiation magnetohydrodynamics. In: Finite volumes for complex applications, III (Porquerolles, 2002). pp. 165–172. Hermes Sci. Publ., Paris (2002).
    2. Ohlberger, M., Rohde, C.: Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems. IMA J. Numer. Anal. 22, 253–280 (2002). https://doi.org/10.1093/imanum/22.2.253.
    3. Lefloch, P.G., Mercier, J.M., Rohde, C.: Fully discrete, entropy conservative schemes of arbitrary order. SIAM J. Numer. Anal. 40, 1968––1992 (electronic) (2002). https://doi.org/10.1137/S003614290240069X.
    4. Freistühler, H., Rohde, C.: Numerical computation of viscous profiles for hyperbolic conservation laws. Math. Comp. 71, 1021––1042 (electronic) (2002). https://doi.org/10.1090/S0025-5718-01-01340-0.

  25. 2001

    1. Haasdonk, B., Kröner, D., Rohde, C.: Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids. Numer. Math. 88, 459–484 (2001). https://doi.org/10.1007/s211-001-8011-x.
    2. Freistühler, H., Fries, C., Rohde, C.: Existence, bifurcation, and stability of profiles for classical and non-classical shock waves. In: Ergodic theory, analysis, and efficient simulation of dynamical systems. pp. 287–309, 814. Springer, Berlin (2001).
    3. LeFloch, P.G., Rohde, C.: Zero diffusion-dispersion limits for self-similar Riemann solutions to hyperbolic systems of conservation laws. Indiana Univ. Math. J. 50, 1707–1743 (2001). https://doi.org/10.1512/iumj.2001.50.2057.
    4. Dedner, A., Kröner, D., Rohde, C., Wesenberg, M.: Godunov-type schemes for the MHD equations. In: Godunov methods (Oxford, 1999). pp. 209–216. Kluwer/Plenum, New York (2001).
    5. Hillen, T., Rohde, C., Lutscher, F.: Existence of weak solutions for a hyperbolic model of chemosensitive movement. J. Math. Anal. Appl. 260, 173–199 (2001). https://doi.org/10.1006/jmaa.2001.7447.
    6. Freistühler, H., Rohde, C.: A numerical study on viscous profiles of MHD shock waves. In: Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000). pp. 399–408. Birkhäuser, Basel (2001).
    7. Dedner, A., Kröner, D., Rohde, C., Wesenberg, M.: MHD instabilities arising in solar physics: a numerical approach. In: Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000). pp. 277–286. Birkhäuser, Basel (2001).
    8. Haasdonk, B., Kröner, D., Rohde, C.: Convergence of a staggered Lax-Friedrichs scheme for nonlinear conservation laws on unstructured two-dimensional grids. Numer. Math. 88, 459–484 (2001). https://doi.org/10.1007/s211-001-8011-x.

  26. 2000

    1. Lefloch, P.G., Rohde, C.: High-order schemes, entropy inequalities, and nonclassical shocks. SIAM J. Numer. Anal. 37, 2023––2060 (electronic) (2000). https://doi.org/10.1137/S0036142998345256.

  27. 1999

    1. Freistühler, H., Rohde, C.: Numerical methods for viscous profiles of non-classical shock waves. In: Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich, 1998). pp. 333–342. Birkhäuser, Basel (1999).
    2. Dedner, A., Rohde, C., Wesenberg, M.: A MHD-simulation in solar physics. In: Finite volumes for complex applications II. pp. 491–498. Hermes Sci. Publ., Paris (1999).

  28. 1998

    1. Rohde, C.: Entropy solutions for weakly coupled hyperbolic systems in several space dimensions. Z. Angew. Math. Phys. 49, 470–499 (1998). https://doi.org/10.1007/s000000050102.
    2. Rohde, C.: Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2D. Numer. Math. 81, 85–123 (1998). https://doi.org/10.1007/s002110050385.

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