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Non-overlapping Schwarz algorithms for the Incompressible Navier-Stokes equations with DDFV discretizations

Thierry Goudon 1 Stella Krell 1, 2 Giulia Lissoni 1, 3
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : We propose and analyze non-overlapping Schwarz algorithms for the domain decomposition of the unsteady incompressible Navier-Stokes problem with Discrete Duality Finite Volume discretizations. The design of suitable transmission conditions for the velocity and the pressure is a crucial issue. We establish the well-posedness of the method and the convergence of the iterative process, pointing out how the numerical fluxes influence the asymptotic problem which is intended to be a discretization of the Navier-Stokes equations on the entire computational domain. Finally we perform some numerical tests to illustrate the behavior of the algorithm.
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https://hal.inria.fr/hal-02448007
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Submitted on : Tuesday, January 21, 2020 - 10:59:52 PM
Last modification on : Monday, October 12, 2020 - 2:28:06 PM
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  • HAL Id : hal-02448007, version 1

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Thierry Goudon, Stella Krell, Giulia Lissoni. Non-overlapping Schwarz algorithms for the Incompressible Navier-Stokes equations with DDFV discretizations. 2020. ⟨hal-02448007⟩

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