Inf-Sup Stability of the Discrete Duality Finite Volume method for the 2D Stokes problem

International audience''Discrete Duality Finite Volume'' schemes (DDFV for short) on general 2D meshes, in particular non conforming ones, are studied for the Stokes problem with Dirichlet boundary conditions. The DDFV method belongs to the class of staggered schemes since the components of the velocity and the pressure are approximated on different meshes. In this paper, we investigate from a numerical and theoretical point of view, whether or not the stability condition holds in this framework for various kind of mesh families. We obtain that different behaviors may occur depending on the geometry of the meshes. For instance, for conforming acute triangle meshes, we prove the unconditional Inf-Sup stability of the scheme, whereas for some conforming or non-conforming Cartesian meshes we prove that Inf-Sup stability holds up to a single unstable pressure mode. In any cases, the DDFV method appears to be very robust

Numerical analysis of the DDFV method for the Stokes problem with mixed Neumann/Dirichlet boundary conditions

International audienceThe aim of this work is to analyze " Discrete Duality Finite Volume " schemes (DDFV for short) on general meshes by adapting the theory known for the linear Stokes problem with Dirichlet boundary conditions to the case of Neu-mann boundary conditions on a fraction of the boundary. We prove well-posedness for stabilized schemes and we derive some error estimates. Finally, we illustrate some numerical results in which we compare stabilized and unstabilized schemes

DDFV method for Navier-Stokes problem with outflow boundary conditions

International audienceWe 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