Low Mach number limit of some staggered schemes for compressible barotropic flows

In this paper, we study the behaviour at low Mach number of numerical schemes based on staggered discretizations for barotropic Navier-Stokes equations. Three time are considered: implicit-in-time scheme and two non-iterative pressure correction schemes. The last differ by discretization convection term: linearly implicit first one, so resulting is unconditionnally stable, explicit second stable under a CFL condition involving material velocity only. We rigorously prove that these three variants asymptotic preserving in following sense: given mesh step, sequence solutions obtained with vanishing numbers tend to solution standard incompressible flows. This convergence result mimicking proof already known continuous case.