Since seminal papers published in the middle of the sixties, low-order staggered schemes for incompressible flow computations have received a considerable attention. The staggered discretization is a space structured or unstructured discretization where the scalar unknowns (the pressure) are located at the cell centers while the vector unknowns (the velocity) are located at the cells faces. This discretization is essentially motivated by the fact that it combines a low computational cost with the so-called inf-sup or LBB stability condition, which prevents from the odd-even decoupling of the pressure. For several years, an important effort has been dedicated to the extension of staggered numerical schemes for the approximation of compressible flows. In this talk, I will focus on the barotropic compressible Navier-Stokes equations. I will prove that, as the Mach number tends to zero, the solution of the implicit staggered scheme for these equations converges towards the solution of the standard staggered scheme for the incompressible Navier-Stokes equations. In particular, the numerical density tends towards a constant as the Mach number tends to zero. Such a result follows from a similar analysis to that of Lions and Masmoudi (1998) at the continuous level for weak solutions of the barotropic compressible Navier-Stokes equations. It extends to other time discretizations such as the so-called pressure-correction scheme (adapted to compressible models). These numerical schemes are used in practice in industrial codes such as CALIF3S, a code developed by the IRSN (French Institut for Radioprotection and Nuclear Safety) for the simulation of deflagrations.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
