High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids

Gautier Dakin; Hervé Jourdren

doi:10.1016/j.crma.2015.11.008

Numerical analysis

High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids

Presented by: the Editorial Board

Gautier Dakin ¹; Hervé Jourdren ¹

¹ CEA, DAM, DIF, 91297 Arpajon, France

Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 211-217.

Abstract
Résumé

We consider a class of staggered grid schemes for solving the 1D Euler equations in internal energy formulation. The proposed schemes are applicable to arbitrary equations of state and high-order accurate in both space and time on smooth flows. Adding a discretization of the kinetic energy equation, a high-order kinetic energy synchronization procedure is introduced, preserving globally total energy and enabling proper shock capturing. Extension to nD Cartesian grids is done via C-type staggering and high-order dimensional splitting. Numerical results are provided up to 8th-order accuracy.

Nous considérons une classe de schémas sur maillage décalé pour résoudre les équations d'Euler 1D. Les schémas proposés, formulés en énergie interne, sont d'ordre élevé en espace comme en temps, utilisables quelle que soit l'équation d'état. En ajoutant une discrétisation de l'équation de l'énergie cinétique, une procédure de synchronisation de l'énergie cinétique est introduite, préservant globalement l'énergie totale et permettant la capture correcte des chocs. Une extension nD sur grille cartésienne décalée de type C avec splitting directionnel d'ordre élevé est proposée. Des résultats numériques sont présentés jusqu'à l'ordre 8.

Received: 2015-07-29
Accepted: 2015-11-19
Published online: 2016-01-18

DOI: 10.1016/j.crma.2015.11.008

Author's affiliations:

Gautier Dakin ¹; Hervé Jourdren ¹

¹ CEA, DAM, DIF, 91297 Arpajon, France

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     author = {Gautier Dakin and Herv\'e Jourdren},
     title = {High-order accurate {Lagrange-remap} hydrodynamic schemes on staggered {Cartesian} grids},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {211--217},
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     doi = {10.1016/j.crma.2015.11.008},
     language = {en},
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Gautier Dakin; Hervé Jourdren. High-order accurate Lagrange-remap hydrodynamic schemes on staggered Cartesian grids. Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 211-217. doi : 10.1016/j.crma.2015.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.11.008/

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