Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations

Free access article

Issue		ESAIM: Proc. Volume 29, 2009 Multiresolution and Adaptive Methods for Convection-Dominated Problems


Page(s)		28 - 42
DOI		http://dx.doi.org/10.1051/proc/2009053
Published online		10 December 2009

ESAIM: Proc., 2009, Vol. 29, pp. 28-42
DOI: 10.1051/proc/2009053

Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations

Ralf Deiterding¹, Margarete O. Domingues^{2, 3}, Sônia M. Gomes⁴, Olivier Roussel^{3, 4} and Kai Schneider^{3, 5}

¹ Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008 MS-6367, Oak Ridge, TN 37831, United States,
    e-mail: deiterdingr@ornl.gov
² Laboratório Associado de Computaçãoe Matemática Aplicada (LAC), Coordenadoria dos Laboratórios Associados (CTE), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas 1758, 12227-010 São José dos Campos, São Paulo, Brazil,
    e-mail: margarete@lac.inpe.br
³ Laboratoire de Modélisation en Mécanique et Procédés Propres (M2P2), CNRS, Universités d'Aix-Marseille et Ecole Centrale Marseille, 38 rue F. Joliot-Curie, 13451 Marseille Cedex 20, France,
    e-mail: o_roussel@yahoo.fr
⁴ Universidade Estadual de Campinas (UNICAMP), IMECC, Caixa Postal 6065, 13083-970 Campinas, São Paulo, Brazil,
    e-mail: soniag@ime.unicamp.br
⁵ Centre de Mathématiques et d'Informatique (CMI), Université de Provence, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France,
    e-mail: kschneid@cmi.univ-mrs.fr

Published online: 10 December 2009

Abstract
We present adaptive multiresolution (MR) computations of the two-dimensional compressible Euler equations for a classical Riemann problem. The results are then compared with respect to accuracy and computational efficiency, in terms of CPU time and memory requirements, with the corresponding finite volume scheme on a regular grid. For the same test case, we also perform computations using adaptive mesh refinement (AMR) imposing similar accuracy requirements. The results thus obtained are compared in terms of computational overhead and compression of the computational grid, using in addition either local or global time stepping strategies. We preliminarily conclude that the multiresolution techniques yield improved memory compression and gain in CPU time with respect to the adaptive mesh refinement method. 

Résumé
Nous présentons des simulations adaptatives multirésolution (MR) des équations d'Euler compressibles bi-dimensionnelles pour un problème de Riemann classique. Les résultats sont comparés en précision et en efficacité – temps CPU et place mémoire – avec ceux obtenus par la méthode volumes finis sur la grille la plus fine. Pour le même cas-test, nous présentons les calculs obtenus à l'aide de la méthode AMR (Adaptive Mesh Refinement) en imposant les mêmes critères de précision. Les résultats ainsi obtenus sont comparés en termes d'effort de calcul et de compression mémoire, en utilisant des pas de temps globaux puis locaux. De ces résultats préliminaires, nous concluons que les techniques multirésolution présentent des gains en termes de temps CPU et de place mémoire supérieurs à ceux de la méthode AMR.

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