We introduce continuous tools to study the low Mach number behavior of the Godunov scheme applied to the linear wave equation with porosity on cartesian meshes. More precisely, we extend the Hodge decomposition to a weighted L space in the continuous case and we study the properties of the modified equation associated to this Godunov scheme. This allows to partly explain the inaccuracy of the G...

We investigate the accuracy of the Godunov scheme applied to the variable cross-section acoustic equations. Contrarily to the constant cross-section case, the accuracy issue of this scheme in the low Mach number regime appears even in the one-dimensional case; on the other hand, we show that it is possible to construct another Godunov type scheme which is accurate in the low Mach number regime.

Through a linear analysis, we show how to modify Godunov type schemes applied to the compressible Euler system to make them accurate at any Mach number. This allows to propose all Mach Godunov type schemes. A linear stability result is proposed and a formal asymptotic analysis justifies the construction in the barotropic case when the Godunov type scheme is a Roe scheme. We also underline that ...

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservati...

As a continuous eeort to understand the Godunov-type schemes, following the paper \Projection in this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers. More speciically, the underlying dynamics of Flux Vector Splitting (FVS) and Flux Diierence Splitting (FDS) schemes will be analyzed. Since the FVS scheme and the Kinetic Flux Vector Splitting (...

In this paper, a numerical scheme is proposed for the multi-fluid compressible flows. This method is applied to the problem of underwater explosion. The proposed scheme is basically the extension of Godunov method in gas dynamic problems to the multifluid environments and is second-order accurate in space. In this method, also, the problem of artificial mixing of two different phases on Euleria...

In this paper, a numerical scheme is proposed for the multi-fluid compressible flows. This method is applied to the problem of underwater explosion. The proposed scheme is basically the extension of Godunov method in gas dynamic problems to the multifluid environments and is second-order accurate in space. In this method, also, the problem of artificial mixing of two different phases on Euleria...