On the behavior of upwind schemes in the low Mach number limit. IV: \P0\ approximation on triangular and tetrahedral cells.

Hervé Guillard (1, 2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 PUMAS - Plasma, tUrbulence, Modeling, Approximation and Simulation

Finite Volume upwind schemes for the Euler equations in the low Mach number regime face a problem of lack of convergence toward the solutions of the incompressible system. However, if applied to cell centered triangular grid, this problem disappears and convergence toward the incompressible solution is recovered. Extending the work of [3] that prove this result for regular triangular grid, we give here a general proof of this fact for arbitrary unstructured meshes. In addition, we also show that this result is equally valid for unstructured three dimensional tetrahedral meshes.

Domaines: Analyse numérique [math.NA]; Physique mathématique [math-ph]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Physique Numérique [physics.comp-ph]

Hervé Guillard. On the behavior of upwind schemes in the low Mach number limit. IV: \P0\ approximation on triangular and tetrahedral cells.. Computers and Fluids, 2009, 38 (10), pp.1969-1972. ⟨10.1016/j.compfluid.2009.06.003⟩. ⟨hal-00871718⟩