In this work we design a new domain decomposition method for the Euler equations in 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 sub-domains, it converges in 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, ).
Mots clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {689--703},
publisher = {EDP-Sciences},
volume = {40},
number = {4},
year = {2006},
doi = {10.1051/m2an:2006026},
mrnumber = {2274774},
zbl = {1173.76381},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2006026/}
}
TY - JOUR AU - Dolean, Victorita AU - Nataf, Frédéric TI - A new domain decomposition method for the compressible Euler equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 689 EP - 703 VL - 40 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006026/ DO - 10.1051/m2an:2006026 LA - en ID - M2AN_2006__40_4_689_0 ER -
%0 Journal Article %A Dolean, Victorita %A Nataf, Frédéric %T A new domain decomposition method for the compressible Euler equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 689-703 %V 40 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006026/ %R 10.1051/m2an:2006026 %G en %F M2AN_2006__40_4_689_0
Dolean, Victorita; Nataf, Frédéric. A new domain decomposition method for the compressible Euler equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 4, pp. 689-703. doi : 10.1051/m2an:2006026. http://www.numdam.org/articles/10.1051/m2an:2006026/
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