Comptes Rendus
Numerical Analysis
High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics
[Schémas directions alternées d'ordre élevé de type Lagrange-projection pour l'hydrodynamique compressible]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 105-110.

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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Accepté le :
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DOI : 10.1016/j.crma.2009.12.008

Frédéric Duboc 1 ; Cédric Enaux 1 ; Stéphane Jaouen 1 ; Hervé Jourdren 1 ; Marc Wolff 1

1 CEA, DAM, DIF, 91297 Arpajon, France
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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/

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