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. Huang, Q., Rohde, C., Yong, W.-A., Zhang, R.: A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility. äccepted for publication in “J. Differential Equations”. (2025).
    3. 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).
    4. 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).
    5. 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).
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    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.: 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.
    12. Mel’nyk, T., Rohde, C.: Muskat-Leverett two-phase flow in thin cylindric porous media: Asymptotic approach, https://arxiv.org/abs/2411.02923, (2024).

  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. 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).
    6. 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.
    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. 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.
    2. 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.
    3. 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).
    4. Giesselmann, J., Meyer, F., Rohde, C.: A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws. BIT Numer. Math. (2020).
    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 multicomponent flow in porous media with Maxwell-Stefan diffusion. Math. Meth. Appl. Sci. 43, 4200–4221 (2020). https://doi.org/10.1002/mma.6185.
    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. 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.
    2. Colombo, R.M., LeFloch, P.G., Rohde, C., Trivisa, K.: Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics. Oberwohlfach Rep. 1419–1497 (2019).
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    3. 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.
    4. 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.
    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., 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).
    6. 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.

  10. 2016

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Kissling, F., Rohde, C.: THE COMPUTATION OF NONCLASSICAL SHOCK WAVES IN POROUS MEDIA WITH A HETEROGENEOUS MULTISCALE METHOD: THE MULTIDIMENSIONAL CASE. MULTISCALE MODELING & SIMULATION. 13, 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. 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).
    9. Corli, A., Rohde, C., Schleper, V.: Parabolic approximations of diffusive-dispersive equations. J. Math. Anal. Appl. 414, 773–798 (2014).

  13. 2013

    1. 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.
    2. 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.
    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. 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).
    2. 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.
    3. 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.
    4. 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.
    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.: 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.
    5. 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.
    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. 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.
    8. 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.

  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. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    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.
  • Summer term 2025
  • Winter term 2024/25
    • Special Aspects of Numerical Mathematics
  • Summer term 2024:
    • Advanced Numerics of Partial Differential Equations
    • Mathematische Methoden in der Strömungsmechanik
    • Seminar für Mehrphasenströmungen
  • Winter term 2023/24:
    • Introduction to the numerics of partial differential equations 
  • Summer term 2023:
    • Numerische Grundlagen für ernen, fmt, mach, mawi
    • Computerpraktikum für den Bachelor
    • Masterseminar Mathematics of Shock Waves 
  • Winter term 2022/23:
    • Numerik für Differentialgleichungen
    • Institutsseminar Angewandte Analysis und Numerische Simulation
    • Seminar für Mehrphasenströmungen
  • Summer term 2022:
    • Numerische Mathematik 2 (Vorlesung und Übung)
    • Proseminar Numerik für Data Sciences
    • Institutsseminasr Angewandte Analysis und Numerische Simulation
    • Mathematische Methoden in der Strömungsmechanik (Vorlesung und Übung)
    • Seminar für Mehrphasenströmungen
    • Fortgeschrittene Analysis für SimTech2 (Vorlesung und Übung)
  • Winter term 2021/22:
    • Numerische Mathematik 1
    • Stochastik und Angewandte Mathematik für das Lehramt (zusammen mit M. Griesemer)
    • Masterseminar Mathematische Modellierung: Grenzflächendynamik: scharf oder diffus?
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