Comptes Rendus
ADER discontinuous Galerkin schemes for aeroacoustics
Comptes Rendus. Mécanique, Volume 333 (2005) no. 9, pp. 683-687.

In this paper we apply the ADER approach to the Discontinuous Galerkin (DG) framework for the two-dimensional linearized Euler equations. The result is an efficient high order accurate single-step scheme in time which uses less storage than Runge–Kutta DG schemes, especially for very high order of accuracy. The aim is to obtain an arbitrarily accurate scheme in space and time on unstructured grids for accurate noise propagation in the time domain in very complex geometries. We will present numerical convergence rates for ADER-DG methods up to 10th order of accuracy in space and time on structured and unstructured meshes.

Nous appliquons l'approche ADER au cadre des éléments finis discontinus pour les équations d'Euler linéarisées bidimensionnelles. Le résultat sont des schémas de haute précision tout en utilisant moins de mémoire que les schémas du type Runge–Kutta Galerkin discontinus, spécialement pour les ordres trés élevés. Le but est d'obtenir un schéma de précision arbitraire en temps et en espace sur des maillages non-structurés pour le calcul précis du bruit dans les géometries très complexes. Nous présentons des études de convergence numériques pour des méthodes ADER-DG sur des maillages structurés et non-structurés jusqu'à l'ordre 10 en temps et en espace.

Published online:
DOI: 10.1016/j.crme.2005.07.008
Keywords: Acoustics, Discontinuous Galerkin schemes, Very high order methods, ADER approach, Unstructured grids
Mot clés : Acoustique, Schémas Galerkin discontinus, Méthodes d'ordre très élevé, Approche ADER, Maillages non-structurés

Michael Dumbser 1; Claus-Dieter Munz 1

1 Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, 70550 Stuttgart, Germany
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Michael Dumbser; Claus-Dieter Munz. ADER discontinuous Galerkin schemes for aeroacoustics. Comptes Rendus. Mécanique, Volume 333 (2005) no. 9, pp. 683-687. doi : 10.1016/j.crme.2005.07.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.07.008/

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