A new domain decomposition method for the compressible Euler equations
Laboratoire de Mathématiques J.A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France. firstname.lastname@example.org
2 Laboratoire J.L. Lions, CNRS UMR 7598, Université Pierre et Marie Curie, Paris 75005, France. email@example.com
Revised: 16 May 2006
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. I 325 (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, ...).
Mathematics Subject Classification: 35M20 / 65M55
Key words: Smith factorization / domain decomposition method / Euler equations.
© EDP Sciences, SMAI, 2006