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Moving-Mesh Finite-Volume Methods for Hyperbolic Interface Dynamics

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Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems (FVCA 2023)

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Abstract

The numerical discretization of continuum-mechanical free boundary value problems for hyperbolic conservation laws becomes challenging when the dynamics of the interface depend sensitively on smaller-scale effects. A proper tracking of the interface and an efficient solution of the conservation laws in the bulk domains can be realized by a heterogeneous multi-scale ansatz combined with recently introduced moving-mesh concepts for finite-volume methods. To illustrate the approach we focus on two applications: the tracking of phase boundaries in compressible liquid-vapour flow and dimensionally mixed models for two-phase flow in fractured porous media. In the first case phase transition effects lead to non-standard interface dynamics. In the latter case the coupling conditions for the bulk domains involve the solution of evolution equations in the fractures which are represented as hypersurfaces.

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Acknowledgements

Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 - 390740016. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech).

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Authors and Affiliations

  1. Institute of Applied Analysis and Numerical Simulation and Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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  1. Christian Rohde
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Correspondence to Christian Rohde .

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Editors and Affiliations

  1. IRMA, Strasbourg, France

    Emmanuel Franck

  2. Weierstrass Institute, Berlin, Germany

    Jürgen Fuhrmann

  3. IRMA, Strasbourg, France

    Victor Michel-Dansac

  4. IRMA, Strasbourg, France

    Laurent Navoret

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Rohde, C. (2023). Moving-Mesh Finite-Volume Methods for Hyperbolic Interface Dynamics. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 432. Springer, Cham. https://doi.org/10.1007/978-3-031-40864-9_7

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