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Journal of Scientific Computing

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04.04.2015

Towards Optimized Schwarz Methods for the Navier–Stokes Equations

verfasst von: Eric Blayo, David Cherel, Antoine Rousseau

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

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Abstract

This paper presents a study of optimized Schwarz domain decomposition methods for Navier–Stokes equations. Once discretized in time, optimal transparent boundary conditions are derived for the resulting Stokes equations, and a series of local approximations for these nonlocal conditions are proposed. Their convergence properties are studied, and numerical simulations are conducted on the test case of the driven cavity with two subdomains. It is shown that conditions involving one or two degrees of freedom can improve the convergence properties of the original algorithm.

Vorheriger Artikel An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

Nächster Artikel Petviashvilli’s Method for the Dirichlet Problem

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We consider here the non symmetric form of the stress tensor. The alternative consisting in using its symmetric form will be discussed in Sect. 5.

For the sake of readability, the Schwarz indices \(m\) and \(m-1\) have been removed, but \(u^{1}\) should be read as \(u^{1,m}\), and \(u^{2}\) as \(u^{2,m-1}\) as in (23a). In the other case (\(u^{1}=u^{1,m-1}\) and \(u^{2}=u^{2,m}\)), we would obtain the discretized version of (24a).

The time steps from \(t=0\) to \(t=1\) have been previously computed with the monodomain algorithm in order to avoid starting from a zero initial solution, which could hide numerical evidences.

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Titel: Towards Optimized Schwarz Methods for the Navier–Stokes Equations
verfasst von: Eric Blayo
David Cherel
Antoine Rousseau
Publikationsdatum: 04.04.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0020-9

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