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
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : 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.
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Thierry Goudon, Stella Krell, Giulia Lissoni. DDFV method for Navier-Stokes problem with outflow boundary conditions. 2018. ⟨hal-01842129⟩

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