A new domain decomposition method for the compressible euler equations using smith factorization

Victorita Dolean, Fŕed́eric Nata

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Abstract

In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The starting point is the equivalence with a third order scalar equation to whom we can apply an algorithm inspired from the Robin- Robin preconditioner for the convection-diffusion equation [1]. Afterwards we translate it into an algorithm for the initial system and prove that at the continuous level and for a decomposition into 2 sub-domains, it converges in 2 iterations. This property cannot be conserved strictly at discrete level and for arbitrary domain decompositions but we still have numerical results which confirm a very good stability with respect to the various parameters of the problem (mesh size, Mach number, ⋯).

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XVII
PublisherSpringer
Pages331-338
Number of pages8
Volume60
ISBN (Print)9783540751984
DOIs
Publication statusPublished - 1 Dec 2008
Event17th International Conference on Domain Decomposition Methods - St. Wolfgang /Strobl, Austria
Duration: 3 Jul 20067 Jul 2006

Publication series

NameLecture Notes in Computational Science and Engineering
Volume60
ISSN (Print)1439-7358

Conference

Conference17th International Conference on Domain Decomposition Methods
CountryAustria
CitySt. Wolfgang /Strobl
Period3/07/067/07/06

Keywords

  • Mach number
  • Euler equation
  • domain decomposition
  • domain decomposition method

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    Dolean, V., & Nata, F. (2008). A new domain decomposition method for the compressible euler equations using smith factorization. In Domain Decomposition Methods in Science and Engineering XVII (Vol. 60, pp. 331-338). (Lecture Notes in Computational Science and Engineering; Vol. 60). Springer. https://doi.org/10.1007/978-3-540-75199-1_40