Geodesic
A new domain decomposition method for the compressible Euler equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 4, pp. 689-703

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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 : 10.1051/m2an:2006026
Classification : 35M20, 65M55
Keywords: Smith factorization, domain decomposition method, Euler equations 
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     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 },
     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://geodesic.mathdoc.fr/articles/10.1051/m2an:2006026/}
}
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Dolean, Victorita; Nataf, Frédéric. A new domain decomposition method for the compressible Euler equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 4, pp. 689-703. doi: 10.1051/m2an:2006026

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