[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 = {Duboc, Fr\'ed\'eric and Enaux, C\'edric and Jaouen, St\'ephane and Jourdren, Herv\'e and Wolff, Marc},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.12.008/}
}
TY - JOUR AU - Duboc, Frédéric AU - Enaux, Cédric AU - Jaouen, Stéphane AU - Jourdren, Hervé AU - Wolff, Marc 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2009.12.008/ DO - 10.1016/j.crma.2009.12.008 LA - en ID - CRMATH_2010__348_1-2_105_0 ER -
%0 Journal Article %A Duboc, Frédéric %A Enaux, Cédric %A Jaouen, Stéphane %A Jourdren, Hervé %A Wolff, Marc %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 %U http://www.numdam.org/articles/10.1016/j.crma.2009.12.008/ %R 10.1016/j.crma.2009.12.008 %G en %F CRMATH_2010__348_1-2_105_0
Duboc, Frédéric; Enaux, Cédric; Jaouen, Stéphane; Jourdren, Hervé; Wolff, Marc. High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics. Comptes Rendus. Mathématique, Tome 348 (2010) no. 1-2, pp. 105-110. doi : 10.1016/j.crma.2009.12.008. http://www.numdam.org/articles/10.1016/j.crma.2009.12.008/
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