Staggered discretizations, pressure correction schemes and all speed barotropic flows

International audienceWe present in this paper a class of schemes for the solution of the barotropic Navier- Stokes equations. These schemes work on general meshes, preserve the stability properties of the continuous problem, irrespectively of the space and time steps, and boil down, when the Mach number vanishes, to discretizations which are standard (and stable) in the incompressible framework. Finally, we show that they are able to capture solutions with shocks to the Euler equation