A simple parameter-free entropy correction for approximate Riemann solvers

Philippe Helluy; Jean-Marc Hérard; Hélène Mathis; Siegfried Müller

doi:10.1016/j.crme.2010.07.007

A simple parameter-free entropy correction for approximate Riemann solvers
[Une correction entropique non paramétrique simple pour les solveurs de Riemann approchés]

Philippe Helluy ¹ ; Jean-Marc Hérard ² ; Hélène Mathis ¹ ; Siegfried Müller ³

¹ IRMA, université de Strasbourg, 7, rue Descartes, 67084 Strasbourg cedex, France
² EDF, recherche et développement, département M.F.E.E., 6, quai Watier, 78401 Chatou cedex, France
³ Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany

Comptes Rendus. Mécanique, Volume 338 (2010) no. 9, pp. 493-498.

Résumé
Abstract

On présente dans cette note une correction entropique non paramétrique simple et générale pour la simulation d'écoulements de fluides comportant des points soniques en zone de détente. Celle-ci permet d'accroître la stabilité et la précision de solveurs de Riemann approchés. Cette correction est aussi appliquée aux équations de la MHD idéale.

We present here a simple and general non-parametrized entropy-fix for the computation of fluid flows involving sonic points in rarefaction waves. It enables to improve the stability and the accuracy of approximate Riemann solvers. It is also applied to MHD flows.

Reçu le : 2009-02-16
Accepté le : 2010-07-07
Publié le : 2010-07-31

DOI : 10.1016/j.crme.2010.07.007

Keywords: Computational fluid mechanics, Approximate Riemann solver, Entropy correction
Mots-clés : Mécanique des fluides numérique, Solveur de Riemann approché, Correction entropique

Affiliations des auteurs :

Philippe Helluy ¹ ; Jean-Marc Hérard ² ; Hélène Mathis ¹ ; Siegfried Müller ³

¹ IRMA, université de Strasbourg, 7, rue Descartes, 67084 Strasbourg cedex, France
² EDF, recherche et développement, département M.F.E.E., 6, quai Watier, 78401 Chatou cedex, France
³ Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany

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     author = {Philippe Helluy and Jean-Marc H\'erard and H\'el\`ene Mathis and Siegfried M\"uller},
     title = {A simple parameter-free entropy correction for approximate {Riemann} solvers},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {493--498},
     publisher = {Elsevier},
     volume = {338},
     number = {9},
     year = {2010},
     doi = {10.1016/j.crme.2010.07.007},
     language = {en},
}

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Philippe Helluy; Jean-Marc Hérard; Hélène Mathis; Siegfried Müller. A simple parameter-free entropy correction for approximate Riemann solvers. Comptes Rendus. Mécanique, Volume 338 (2010) no. 9, pp. 493-498. doi : 10.1016/j.crme.2010.07.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.007/

Bibliographie
Cité par

[1] S. Godunov A difference method for numerical calculation of discontinuous equations of hydrodynamics, Mat. Sb., Volume 47 (1959), pp. 217-300

[2] P.L. Roe Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys., Volume 43 (1981), pp. 357-372

[3] V.V. Rusanov Calculation of interaction of non steady shock waves with obstacles, J. Comput. Math. Phys., Volume 1 (1961), pp. 267-279

[4] T. Gallouët; J.M. Hérard; N. Seguin Some recent Finite Volume schemes to compute Euler equations with real gas EOS, Internat. J. Numer. Methods Fluids, Volume 39 (2002), pp. 1073-1138

[5] A. Harten; J.M. Hyman A self-adjusting grid for the computation of weak solutions of hyperbolic conservation laws, J. Comput. Phys., Volume 50 (1983), pp. 235-269

[6] F. Dubois; G. Mehlman A non-parametrized entropy correction for Roe's approximate Riemann solver, Numer. Math., Volume 73 (1996), pp. 169-208

[7] T. Gallouët; J.M. Masella A rough Godunov scheme, CRAS Paris I, Volume 323 (1996), pp. 77-84

[8] T. Buffard; T. Gallouët; J.M. Hérard A sequel to a rough Godunov scheme. Application to real gases, Comput. and Fluids, Volume 29 (2000), pp. 813-847

[9] C. Altmann; T. Belat; M. Gutnic; P. Helluy; H. Mathis; É. Sonnendrücker; W. Angulo; J.-M. Hérard A local time-stepping discontinuous Galerkin algorithm for the MHD system, ESAIM Proc., Volume 28 (2009), pp. 33-54

[10] P. Helluy; J.M. Hérard; H. Mathis A well-balanced approximate Riemann solver for variable cross-section compressible flows, 2009 http://www.aiaa.org (AIAA Paper 2009-3540)

[11] J.M. Hérard, M. Uhlmann, D. van der Velden, Numerical techniques for solving hybrid Euler–Lagrange models for particulate flows, EDF report H-I81-2009-3961-EN, 2009.

[12] A. Dedner; F. Kemm; D. Kröner; C.-D. Munz; T. Schnitzer; M. Wesenberg Hyperbolic divergence cleaning for the MHD equations, J. Comput. Phys., Volume 175 (2002) no. 2, pp. 645-673

[13] P. Cargo; G. Gallice Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws, J. Comput. Phys., Volume 136 (1997) no. 2, pp. 446-466

[14] M. Torrilhon Uniqueness conditions for Riemann problems of ideal magnetohydrodynamics, J. Plasma Phys., Volume 69 (2003) no. 3, pp. 253-276

[15] F. Bouchut; C. Klingenberg; K. Waagan A multiwave approximate Riemann solver for ideal MHD based on relaxation. I. Theoretical framework, Numer. Math., Volume 108 (2007) no. 1, pp. 7-42

J. Bussac; H. Mathis Simulation of a homogeneous relaxation model for a three-phase mixture with miscible phases, Computers Mathematics with Applications, Volume 143 (2023), p. 327 | DOI:10.1016/j.camwa.2023.05.012
Christophe Berthon; Manuel J. Castro Díaz; Arnaud Duran; Tomás Morales de Luna; Khaled Saleh Artificial Viscosity to Get Both Robustness and Discrete Entropy Inequalities, Journal of Scientific Computing, Volume 97 (2023) no. 3 | DOI:10.1007/s10915-023-02385-1
Jeremy C.H. Wang; Jean-Pierre Hickey A class of structurally complete approximate Riemann solvers for trans- and supercritical flows with large gradients, Journal of Computational Physics, Volume 468 (2022), p. 111521 | DOI:10.1016/j.jcp.2022.111521
Sergey Gavrilyuk; Jean-Marc Hérard; Olivier Hurisse; Ali Toufaili Theoretical and Numerical Analysis of a Simple Model Derived from Compressible Turbulence, Journal of Mathematical Fluid Mechanics, Volume 24 (2022) no. 2 | DOI:10.1007/s00021-022-00676-5
Jeremy C. H. Wang; Jean Pierre Hickey A Class of Structurally Complete Approximate Riemann Solvers for Trans- and Supercritical Flows with Large Gradients, SSRN Electronic Journal (2022) | DOI:10.2139/ssrn.4010625
Christophe Berthon; Arnaud Duran; Khaled Saleh An Easy Control of the Artificial Numerical Viscosity to Get Discrete Entropy Inequalities When Approximating Hyperbolic Systems of Conservation Laws, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy (2020), p. 29 | DOI:10.1007/978-3-030-38870-6_5
Christophe Berthon; Arnaud Duran; Françoise Foucher; Khaled Saleh; Jean De Dieu Zabsonré Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities, Journal of Scientific Computing, Volume 80 (2019) no. 2, p. 924 | DOI:10.1007/s10915-019-00961-y
Olivier Hurisse Numerical simulations of steady and unsteady two-phase flows using a homogeneous model, Computers Fluids, Volume 152 (2017), p. 88 | DOI:10.1016/j.compfluid.2017.04.007
K. Dorogan; M. Guingo; J.M. Hérard; J.P. Minier A relaxation scheme for hybrid modelling of gas-particle flows, Computers Fluids, Volume 70 (2012), p. 148 | DOI:10.1016/j.compfluid.2012.09.015
Philippe Helluy; Jean-Marc Hérard; Hélène Mathis A well-balanced approximate Riemann solver for compressible flows in variable cross-section ducts, Journal of Computational and Applied Mathematics, Volume 236 (2012) no. 7, p. 1976 | DOI:10.1016/j.cam.2011.11.008

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