no. 4
Non-overlapping Schwarz algorithms for the incompressible Navier–Stokes equations with DDFV discretizations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 4, pp. 1271-1321

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021024
Classification : 65M08, 35Q30, 76D05
Keywords: DDFV methods, domain decomposition, simulation of incompressible viscous flows 
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     title = {Non-overlapping {Schwarz} algorithms for the incompressible {Navier{\textendash}Stokes} equations with {DDFV} discretizations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1271--1321},
     year = {2021},
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Goudon, Thierry; Krell, Stella; Lissoni, Giulia. Non-overlapping Schwarz algorithms for the incompressible Navier–Stokes equations with DDFV discretizations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 4, pp. 1271-1321. doi: 10.1051/m2an/2021024

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