Non-overlapping Schwarz algorithms for the incompressible Navier–Stokes equations with DDFV discretizations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2021

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

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 (DDFV) discretization. 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 numerically illustrate the behavior and performances of the algorithm. We discuss on numerical grounds the impact of the parameters for several mesh geometries and we perform simulations of the flow past an obstacle with several domains.
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Dates and versions

hal-03350932 , version 1 (21-09-2021)

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Thierry Goudon, Stella Krell, Giulia Lissoni. Non-overlapping Schwarz algorithms for the incompressible Navier–Stokes equations with DDFV discretizations. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (4), pp.1271-1321. ⟨10.1051/m2an/2021024⟩. ⟨hal-03350932⟩
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