Construction of Godunov type schemes accurate at any Mach number
نویسندگان
چکیده
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 have to introduce a cut-off in the all Mach correction to avoid the creation of non-entropic shock waves.
منابع مشابه
On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes
This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order OðM Þ where M is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order OðM2 Þ. We then propose to modify the fluxes computed by Godunov type schemes by so...
متن کاملOn the Godunov Scheme Applied to the Variable Cross-Section Linear Wave Equation
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.
متن کاملPreliminary Results for the Study of the Godunov Scheme Applied to the Linear Wave Equation with Porosity at Low Mach Number
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...
متن کاملOn entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes
This paper addresses entropy generation and the corresponding dissipation of kinetic energy associated with high-resolution, shock-capturing (Godunov) methods. Analytical formulae are derived for the rate of increase of entropy given arbitrary jumps in primitive variables at a cell interface. It is demonstrated that for general continuously varying flows the inherent numerical entropy increase ...
متن کاملTime-splitting framework for Godunov-type finite- volume non-hydrostatic atmospheric models
Highorder extensions of the classical Godunov scheme offer computationally attractive features including inherent conservation, geometric flexibility, and accuracy for solving hyperbolic conservation laws. The Godunov-type methods typically do not rely on staggered grids, and the cellaveraged solution is not assumed to be continuous across the cell (control volume) edges. The discontinuity of t...
متن کامل