Preliminary assessment of a new algorithm for the MHD equations at all Mach number regimes

In this paper we present a method for solving the compressible MHD equations at arbitrary Mach number flows. Our method is based on the well-known PISO algorithm, which is a pressure based solver. In order to handle all the possible discontinuities that can be generated by the hyperbolic system of MHD equations the AUSMPWMHD technique is applied for the flux calculation. It allows us to obtain conservative fluxes and face values for pressure that are then inserted in the solution algorithm. Regarding validation, two sets of test cases will be addressed. The first one is the 1D Riemann problem, which is tackled using both 1D and 2D formulations for the MHD equations. The second is the 1D and 2D Alfvén waves test case, which will serve to assess the accuracy of the method in smooth flows.