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A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics

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  • Abgrall, Rémi
  • Busto, Saray
  • Dumbser, Michael

Abstract

We introduce a simple and general framework for the construction of thermodynamically compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems that satisfy an extra conservation law. As a particular example in this paper, we consider the general Godunov-Peshkov-Romenski (GPR) model of continuum mechanics that describes the dynamics of nonlinear solids and viscous fluids in one single unified mathematical formalism.

Suggested Citation

  • Abgrall, Rémi & Busto, Saray & Dumbser, Michael, 2023. "A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007020
    DOI: 10.1016/j.amc.2022.127629
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    References listed on IDEAS

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    1. Ray, Deep & Chandrashekar, Praveen, 2017. "An entropy stable finite volume scheme for the two dimensional Navier–Stokes equations on triangular grids," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 257-286.
    2. Gassner, Gregor J. & Winters, Andrew R. & Kopriva, David A., 2016. "A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 291-308.
    3. Busto, S. & Río-Martín, L. & Vázquez-Cendón, M.E. & Dumbser, M., 2021. "A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes," Applied Mathematics and Computation, Elsevier, vol. 402(C).
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    Cited by:

    1. Firas Dhaouadi & Michael Dumbser, 2023. "A Structure-Preserving Finite Volume Scheme for a Hyperbolic Reformulation of the Navier–Stokes–Korteweg Equations," Mathematics, MDPI, vol. 11(4), pages 1-25, February.

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