A low Mach correction for the Godunov scheme applied to the linear wave equation with porosity
Abstract
We study the low Mach number behavior of the Godunov finite volume scheme applied to the linear wave equation with
porosity. More precisely, we extend the Hodge decomposition to a weighted L2 space. We illustrate the influence of the cell
geometry on the accuracy property at low Mach number. In the triangular case, the stationary space of the Godunov scheme
approaches well enough the continuous space of constant pressure and divergent-free velocity while this is not the case in the
Cartesian case. We study the properties of the modified equation associated to this Godunov scheme and we propose some
correction that is continuous with respect to the Mach number.