Improving shock irregularities based on the characteristics of the MHD equations

We have developed a numerical simulation scheme for three-dimensional magnetohydrodynamical flow with shocks. The numerical scheme is based on the Roe-type scheme and includes additional numerical diffusion in the direction tangential to the shock front to care the carbuncle instability. The numerical viscosity is added only in the regions where the characteristics of either fast or slow wave converges, i.e., in the regions potentially dangerous to the carbuncle instability. Accordingly the numerical viscosity is as small as that of the Roe scheme except near the shock fronts. It is demonstrated from comparison with the HLLE scheme that the magnetic Reynolds number is higher in the simulations obtained with our scheme. We show application of the scheme to the magnetohydrodynamical simulations of type II supernova. It is also proved that the scheme is free from the odd–even decoupling.