Geodesic
Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations
Ralf Deiterding1 ; Margarete O. Domingues2, 3 ; Sônia M. Gomes4 ; Olivier Roussel3, 4 ; Kai Schneider3, 5
1Computer 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
2Laboratório 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
3Laboratoire 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
4Universidade Estadual de Campinas (UNICAMP), IMECC, Caixa Postal 6065, 13083-970 Campinas, São Paulo, Brazil, e-mail: soniag@ime.unicamp.br
5Centre 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
ESAIM. Proceedings, Tome 29 (2009), pp. 28-42
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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.

DOI : 10.1051/proc/2009053

Ralf Deiterding  1   ; Margarete O. Domingues  2 , 3   ; Sônia M. Gomes  4   ; Olivier Roussel  3 , 4   ; 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 
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     author = {Ralf Deiterding and Margarete O. Domingues and S\^onia M. Gomes and Olivier Roussel and Kai Schneider},
     title = {Adaptive multiresolution or adaptive mesh refinement? {A} case study for {2D} {Euler} equations},
     journal = {ESAIM. Proceedings},
     pages = {28--42},
     year = {2009},
     volume = {29},
     doi = {10.1051/proc/2009053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009053/}
}
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Ralf Deiterding; Margarete O. Domingues; Sônia M. Gomes; Olivier Roussel; Kai Schneider. Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations. ESAIM. Proceedings, Tome 29 (2009), pp. 28-42. doi: 10.1051/proc/2009053

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