A new domain decomposition method for the compressible Euler equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 4, p. 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, $...$).

DOI : https://doi.org/10.1051/m2an:2006026
Classification:  35M20,  65M55
Keywords: Smith factorization, domain decomposition method, Euler equations
@article{M2AN_2006__40_4_689_0,
author = {Dolean, Victorita and Nataf, Fr\'ed\'eric},
title = {A new domain decomposition method for the compressible Euler equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {40},
number = {4},
year = {2006},
pages = {689-703},
doi = {10.1051/m2an:2006026},
zbl = {1173.76381},
zbl = {pre05122051},
mrnumber = {2274774},
language = {en},
url = {http://www.numdam.org/item/M2AN_2006__40_4_689_0}
}

Dolean, Victorita; Nataf, Frédéric. A new domain decomposition method for the compressible Euler equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 4, pp. 689-703. doi : 10.1051/m2an:2006026. http://www.numdam.org/item/M2AN_2006__40_4_689_0/

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