Comparison of cell-centered and staggered pressure-correction schemes for all-mach flows

Abstract

Defining a robust scheme for solving the compressible Euler equations at all-Mach number is a challenging issue. We consider here an original pressurecorrection scheme which solves the internal energy using a specific corrective term, ensuring the positivity of the internal energy and the global consistency of the scheme. The scheme has already proved its effectiveness on several Riemann problems with both staggered and cell-centered discretizations. We test here these two discretizations against the incompressible limit of the Euler equations.