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.
Accepted:
Published online:
Stéphane Del Pino 1; Hervé Jourdren 1
@article{CRMATH_2006__342_6_441_0, author = {St\'ephane Del Pino and Herv\'e Jourdren}, title = {Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics}, journal = {Comptes Rendus. Math\'ematique}, pages = {441--446}, publisher = {Elsevier}, volume = {342}, number = {6}, year = {2006}, doi = {10.1016/j.crma.2006.01.013}, language = {en}, }
TY - JOUR AU - Stéphane Del Pino AU - Hervé Jourdren TI - Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics JO - Comptes Rendus. Mathématique PY - 2006 SP - 441 EP - 446 VL - 342 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2006.01.013 LA - en ID - CRMATH_2006__342_6_441_0 ER -
%0 Journal Article %A Stéphane Del Pino %A Hervé Jourdren %T Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics %J Comptes Rendus. Mathématique %D 2006 %P 441-446 %V 342 %N 6 %I Elsevier %R 10.1016/j.crma.2006.01.013 %G en %F CRMATH_2006__342_6_441_0
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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