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A New Domain Decomposition Method for the Compressible Euler Equations

Victorita Dolean·Frédéric Nataf
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Abstract

In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The basis is the equivalence via the Smith factorization with a third order scalar equation to whom we can apply an algorithm inspired from the Robin-Robin preconditioner for the convection-diffusion equation. 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 preserved 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, ....).

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Victorita Dolean, Frédéric Nataf. 2005-02-22. A New Domain Decomposition Method for the Compressible Euler Equations. https://arxiv.org/abs/math/0502450

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