DDFV method for Navier-Stokes problem with outflow boundary conditions

Thierry Goudon (1) , Stella Krell (2) , Giulia Lissoni (1)

1 COFFEE - COmplex Flows For Energy and Environment
2 LJAD - Laboratoire Jean Alexandre Dieudonné

We propose a Discrete Duality Finite Volume scheme (DDFV for short) for the unsteady incom-pressible Navier-Stokes problem with outflow boundary conditions. As in the continuous case, those conditions are derived from a weak formulation of the equations and they provide an energy estimate of the solution. We prove wellposedness of the scheme and a discrete energy estimate. Finally we perform some numerical tests simulating the flow behind a cylinder inside a long channel to show the robustness of such conditions in the DDFV framework.

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

Thierry Goudon, Stella Krell, Giulia Lissoni. DDFV method for Navier-Stokes problem with outflow boundary conditions. Numerische Mathematik, 2019. ⟨hal-01842129⟩