[Schémas directions alternées d'ordre élevé de type Lagrange-projection pour l'hydrodynamique compressible]
Nous proposons une nouvelle souche de schémas volumes finis pour résoudre les équations d'Euler 1D. Ces schémas, basés sur le formalisme Lagrange-projection, sont d'ordre élevé en régime non linéaire et en formulation équation d'état arbitraire. Une extension multidimensionnelle par splitting directionnel d'ordre élevé sur grille cartésienne est alors proposée, illustrée de résultats numériques jusqu'à l'ordre 6.
We first propose a new class of finite volume schemes for solving the 1D Euler equations. Applicable to arbitrary equations of state, these schemes are based on a Lagrange-remap approach and are high-order accurate in both space and time in the nonlinear regime. A multidimensional extension on nD Cartesian grids is then proposed, using a high-order dimensional splitting technique. Numerical results up to 6th-order are provided.
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@article{CRMATH_2010__348_1-2_105_0,
author = {Fr\'ed\'eric Duboc and C\'edric Enaux and St\'ephane Jaouen and Herv\'e Jourdren and Marc Wolff},
title = {High-order dimensionally split {Lagrange-remap} schemes for compressible hydrodynamics},
journal = {Comptes Rendus. Math\'ematique},
pages = {105--110},
publisher = {Elsevier},
volume = {348},
number = {1-2},
year = {2010},
doi = {10.1016/j.crma.2009.12.008},
language = {en},
}
TY - JOUR AU - Frédéric Duboc AU - Cédric Enaux AU - Stéphane Jaouen AU - Hervé Jourdren AU - Marc Wolff TI - High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics JO - Comptes Rendus. Mathématique PY - 2010 SP - 105 EP - 110 VL - 348 IS - 1-2 PB - Elsevier DO - 10.1016/j.crma.2009.12.008 LA - en ID - CRMATH_2010__348_1-2_105_0 ER -
%0 Journal Article %A Frédéric Duboc %A Cédric Enaux %A Stéphane Jaouen %A Hervé Jourdren %A Marc Wolff %T High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics %J Comptes Rendus. Mathématique %D 2010 %P 105-110 %V 348 %N 1-2 %I Elsevier %R 10.1016/j.crma.2009.12.008 %G en %F CRMATH_2010__348_1-2_105_0
Frédéric Duboc; Cédric Enaux; Stéphane Jaouen; Hervé Jourdren; Marc Wolff. High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 105-110. doi : 10.1016/j.crma.2009.12.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.008/
[1] The Runge–Kutta discontinuous Galerkin method for conservation laws. V – Multidimensional systems, J. Comput. Phys., Volume 141 (1998), pp. 199-224
[2] Artificial fluid properties for large-eddy simulation of compressible turbulent mixing, Phys. Fluids, Volume 19 (2007) no. 055103, pp. 1-9
[3] Arbitrary high-order schemes for the linear advection and wave equations: Application to hydrodynamics and aeroacoustics, C. R. Acad. Sci. Paris, Volume 342 (2006), pp. 441-446
[4] Fourth-order symplectic integration, Physica D, Volume 43 (1990), pp. 105-117
[5] Dissipative issue of high-order shock capturing schemes with non-convex equation of state, J. Comput. Phys., Volume 228 (2009), pp. 833-860
[6] Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput., Volume 19 (1998) no. 6, pp. 1892-1917
[7] The accuracy of symplectic integrators, Nonlinearity, Volume 5 (1992), pp. 541-562
[8] Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Springer, 1998, pp. 325-432
[9] ADER schemes for three-dimensional non-linear hyperbolic systems, J. Comput. Phys., Volume 204 (2005), pp. 715-736
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High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids
Gautier Dakin; Hervé Jourdren
C. R. Math (2016)