Comptes Rendus
Numerical Analysis
Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics
Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 441-446.

We present here an extension to any order of accuracy of the schemes proposed in Daru and Tenaud [J. Comput. Phys. 193 (2) (2004) 563–594] for the linear advection equation in 1D. Such schemes are then used for a high-order generalization of the Godunov method in the case of the wave equation and the locally linearized Euler equations.

On propose ici une extension à un ordre arbitraire des schémas proposés dans Daru et Tenaud [J. Comput. Phys. 193 (2) (2004) 563–594] pour l'advection à vitesse uniforme en 1D. Les schémas obtenus sont alors utilisés pour une généralisation d'ordre élevée du schéma de Godunov dans le cas de l'équation des ondes et des équations d'Euler linéarisées localement.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.01.013

Stéphane Del Pino 1; Hervé Jourdren 1

1 CEA/DAM-Île de France, département sciences de la simulation et de l'information, BP12, 91680 Bruyères-Le-Châtel, France
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Stéphane Del Pino; Hervé Jourdren. Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics. Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 441-446. doi : 10.1016/j.crma.2006.01.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.013/

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[6] P. Lax; B. Wendroff Systems of conservation laws, Comm. Pure Appl. Math., Volume 13 (1960), pp. 217-237

[7] A. Suresh; H.T. Huynh Accurate monotonicity-preserving schemes with Runge–Kutta time stepping, J. Comput. Phys., Volume 136 (1997), pp. 83-99

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