A new domain decomposition method for the compressible euler equations using smith factorization

Dolean, Victorita and Nata, Fŕed́eric; (2008) A new domain decomposition method for the compressible euler equations using smith factorization. In: Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, 60 . Springer, AUT, pp. 331-338. ISBN 9783540751984 (https://doi.org/10.1007/978-3-540-75199-1_40)

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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 [1]. 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, ⋯).

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