A new domain decomposition method for the compressible Euler equations

Victorita Dolean, Frédéric Nataf

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8 Citations (Scopus)


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, ...).

Original languageEnglish
Pages (from-to)689-703
Number of pages15
JournalMathematical Modelling and Numerical Analysis
Issue number4
Publication statusPublished - 31 Aug 2006


  • domain decomposition method
  • Euler equations
  • Smith factorization

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