Diffusion regulation for Euler solvers

A diffusion regulation parameter, which operates based on the jump in the Mach number, is presented for implementation in Euler solvers. This diffusion regulation parameter adjusts itself automatically in different regimes of the flow and leads to the exact capturing of steady contact discontinuities which are aligned with the grid-lines. This diffusion regulator parameter reduces numerical dissipation, is very simple and can be easily incorporated in any Euler solver. By coupling such a parameter with a simple numerical method like the Local Lax-Friedrichs (Rusanov) method, an accurate and yet simple numerical method is developed for the numerical simulation of inviscid compressible fluid flows. To demonstrate the applicability of this approach to any Euler solver, the diffusion regulation parameter is also applied in the framework of a Kinetic Scheme which is very diffusive and the improvements in the accuracy for both the methods are demonstrated through several bench-mark test problems.