Voigt regularization for the explicit time stepping of the Hall effect term

Abstract

ABSTRACTThis article studies the stabilization of the explicit time stepping methods for Hall Maxwell and incompressible Hall MHD equations. Since the Hall effect term contains two spatial derivatives, classical time-stepping schemes result in very restrictive CFL condition. We consider weakening the restrictive time step condition via Voigt regularization. We establish the energy stability result and validate our approach numerically. Numerical experiments demonstrate that we are able to take larger time steps, compared to classical schemes, at additional, negligible computational cost.