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A new domain decomposition method for the compressible Euler equations

Published online by Cambridge University Press:  15 November 2006

Victorita Dolean  and
Frédéric Nataf
Victorita Dolean
Affiliation:
Laboratoire de Mathématiques J.A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France. dolean@math.unice.fr
Frédéric Nataf
Affiliation:
Laboratoire J.L. Lions, CNRS UMR 7598, Université Pierre et Marie Curie, Paris 75005, France. nataf@ann.jussieu.fr
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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 [Achdou and Nataf, C. R. Acad. Sci. Paris Sér. I325 (1997) 1211–1216]. 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, ...).

Keywords

Smith factorizationdomain decomposition methodEuler equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 4 , July 2006 , pp. 689 - 703
Copyright
© EDP Sciences, SMAI, 2006

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