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

This 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.     

EVALUATION OF SOME IMPLICIT TIME-STEPPING ALGORITHMS FOR PSEUDODYNAMIC TESTS

Two types of implicit time-stepping algorithms have been proposed recently for pseudodynamic tests. The first type consists of an algorithm which relies on Newton iterations to satisfy the equations of motion. The second type consists of an algorithm which is based on the Operator-Splitting technique and does not require any numerical iteration. While one or the other has been preferred by some researchers, these time-stepping algorithms have not been analysed and compared under a uniform setting. In this paper, a concise summary of these schemes is presented, and they are evaluated in a consistent manner in terms of numerical dissipation, frequency distortion and experimental errors. The analytical results are validated by numerical simulations as well as experimental results. It is shown that the algorithm based on Newton iterations can control experimental error effects effectively by means of an error-correction procedure. The algorithm based on the Operator-Splitting technique demonstrates similar performance provided the I-Modification is adopted.