| Issue |
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
|
|
|---|---|---|
| Page(s) | 1271 - 1321 | |
| DOI | https://doi.org/10.1051/m2an/2021024 | |
| Published online | 07 July 2021 | |
Non-overlapping Schwarz algorithms for the incompressible Navier–Stokes equations with DDFV discretizations
1
Université Côte d’Azur, Inria, CNRS, LJAD, Sophia Antipolis Cedex, France.
2
Université de Nantes, LMJL, CNRS, Nantes, France.
* Corresponding author: thierry.goudon@inria.fr
Received:
20
April
2020
Accepted:
22
May
2021
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.
Mathematics Subject Classification: 65M08 / 35Q30 / 76D05
Key words: DDFV methods / domain decomposition / simulation of incompressible viscous flows
© The authors. Published by EDP Sciences, SMAI 2021
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