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
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

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