Section: New Results

Relaxation method for Euler/MHD in low-Mach regime

Participants: E. Franck, L. Navoret, F. Bouchut (Marne la Vallée university).

Previously, we have proposed implicit relaxation methods for fluid models that allow us to reverse a simple system. However, previous methods [5] were not very effective in the multi-scale regimes of interest. We therefore proposed a semi-implicit scheme based on a dynamic splitting and a relaxation of fast waves only. The scheme was first applied to the Euler equations in low Mach regime. The scheme is stable and accurate regardless of the Mach number. We have successfully applied the method for the equilibria of the Shallow Water equations. Since last summer we have begun the extension for the 1D MHD with and without dispersive effects. The first results show that we obtain a similar method compared to the Euler case with acceptable stability conditions as for the Euler equations.