A New Domain Decomposition Method for the Compressible Euler Equations
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, ....).
Cite
@article{arxiv.math/0502450,
title = {A New Domain Decomposition Method for the Compressible Euler Equations},
author = {Victorita Dolean and Frédéric Nataf},
journal= {arXiv preprint arXiv:math/0502450},
year = {2009}
}
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