Monday 16th April 2018
François Bouchut Université Paris-Est – Marne-la-Vallée

Title: An explicit second order entropic scheme for incompressible Navier-Stokes

Abstract: We show how a numerical Mach low limit can be used to construct explicit schemes for incompressible Navier-Stokes equations (artificial compressibility method). A kinetic/flow decomposition approach is used at the compressible approximation level.
The resulting scheme satisfies a discrete entropy inequality under a parabolic CFL condition and a stability condition of a Reynolds number associated with the meshes, which ensures that viscosity dominates advection at mesh size. This ensures the robustness of the method, with uniform terminals on the solution.
By choosing the parameters in a relevant way we obtain the order two in space.
The method is evaluated on classical tests with tie-points and in moderately turbulent regime for Reynolds numbers of a few hundred.

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