A sonic fix for ideal magnetogasdynamics equations using the Harten–Yee TVD scheme

Computational magnetogasdynamics (MGD) represents one of the most promising interdisciplinary computational technologies for aerospace design. However, the numerical techniques developed for the MGD equations must be able to solve correctly nonlinear hyperbolic differential equation system. In this work we present a modification of the original Harten–Yee scheme by incorporating a new sonic fix for the acoustic causality points using the finite volume technique. The proposed technique is used to simulate the coplanar MGD Riemann problem where results using the new sonic fix are compared with those given by the traditional Harten–Yee scheme. The obtained 2-D numerical results correctly satisfy the 1-D numerical solutions, and the oscillations present using the Harten–Yee traditional scheme, are reduced.