A new domain decomposition method for the compressible Euler equations

Victorita Dolean, Frédéric Nataf

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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, ...).

LanguageEnglish
Pages689-703
Number of pages15
JournalMathematical Modelling and Numerical Analysis
Volume40
Issue number4
DOIs
Publication statusPublished - 31 Aug 2006

Fingerprint

Compressible Euler Equations
Domain decomposition methods
Euler equations
Domain Decomposition Method
Decomposition
Convection-diffusion Equation
Domain Decomposition
Euler Equations
Preconditioner
Mach number
Strictly
Equivalence
Scalar
Mesh
Converge
Iteration
Decompose
Numerical Results
Arbitrary
Design

Keywords

  • domain decomposition method
  • Euler equations
  • Smith factorization

Cite this

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A new domain decomposition method for the compressible Euler equations. / Dolean, Victorita; Nataf, Frédéric.

In: Mathematical Modelling and Numerical Analysis, Vol. 40, No. 4, 31.08.2006, p. 689-703.

Research output: Contribution to journalArticle

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