Validation of the Semi-Implicit Algorithm Time Stepping for MH4D

Abstract

We present the validation of the semi-implicit time stepping method for MH4D, a resistive magnetohydrodynamic finite volume code on a tetrahedral unstructured mesh. The time steps for standard explicit methods, which are constrained by the Courant–Friedrichs–Lewy (CFL) condition, are typically small for simulations of EC experiments due to the large sound and Alfven speeds. The CFL constraint on time stepping is more severe with a tetrahedral mesh. The implemented semi-implicit algorithm removes these fast waves constraint, thus allowing for larger time steps. For our validation problems, we see a significant increase in time step size due to the semi-implicit time stepping without effecting the physics.