Convergence Analysis of a Schwarz Type Domain Decomposition Method for the Solution of the Euler Equations

Abstract : we report on a preliminary convergence analysis of a domain decomposition method for solving the Euler equations for compressible flows. This method was previously described in Dolean and Lanteri. It relies on the formulati- on of an additive Schwarz type algorithm on a non-overlapping decomposition of the computational domain. According to the hyperbolic nature of the Euler equations, the transmission conditions that are set at subdomain interfaces, express the conservation of the normal flux. In [3], this method is assessed experimentally in the context of a flow solver which is based on a mixed finite volume/finite element formulation on unstructured triangular meshes. Here, we study the convergence of the proposed method in the two- and three-dimensional cases, and for a two-subdomain decomposition, by considering the linearized equations and applying a Fourier analysis. In doing so, we observe that in spite of the fact that we use simple transmission conditions, the method converges and demonstates, for particular flow conditions, an optimal convergence rate. Various numerical experiments allow to exhibit at least qualitatively, the convergence behavior obtained analytically.
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Rapport
[Research Report] RR-3916, INRIA. 2000, pp.45
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https://hal.inria.fr/inria-00072737
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Soumis le : mercredi 24 mai 2006 - 10:45:50
Dernière modification le : vendredi 12 janvier 2018 - 01:51:27
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:20:17

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  • HAL Id : inria-00072737, version 1

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V. Dolean, Stephane Lanteri, Frédéric Nataf. Convergence Analysis of a Schwarz Type Domain Decomposition Method for the Solution of the Euler Equations. [Research Report] RR-3916, INRIA. 2000, pp.45. 〈inria-00072737〉

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