A new domain decomposition method for the compressible Euler equations

Dolean, Victorita; Nataf, Frédéric

ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 4, pp. 689-703.

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, $...$).

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