Adaptive Method of Lines for Magneto-Hydrodynamic PDE Models

Abstract

An adaptive grid technique for use in the solution of multi-dimensional time-dependent PDEs is applied to several magnetohydrodynamic model problems. The technique employs the method-of-lines and can be viewed both in a continuous and semi-discrete setting. By using an equidistribution principle, it has the ability to track individual features of the physical solutions in the developing plasma ows. Moreover, it can be shown that the underlying grid varies smoothly in time and space. The results of several numerical experiments are presented which cover many aspects typifying nonlinear magneto- uid dynamics.