An indirect ALE discretization of single fluid plasma without a fast magnetosonic time step restriction

Abstract

In this paper we present an adjustment to traditional ALE discretizations of resistive MHD where we do not neglect the time derivative of the electric displacement field. This system is referred to variously as a perfect electromagnetic fluid or a single fluid plasma although we refer to the system as Full Maxwell Hydrodynamics (FMHD) in order to evoke its similarities to resistive Magnetohydrodynamics (MHD). Unlike the MHD system the characteristics of this system do not become arbitrarily large in the limit of low densities. In order to take advantage of these improved characteristics of the system we must tightly couple the electromagnetics into the Lagrangian motion and do away with more traditional operator splitting. We provide a number of verification tests to demonstrate both accuracy of the method and an asymptotic preserving (AP) property. In addition we present a prototype calculation of a Z-pinch and find very good agreement between our algorithm and resistive MHD. Further, FMHD leads to a large performance gain (approximately 4.6x speed up) compared to resistive MHD. We unfortunately find our proposed algorithm does not conserve charge leaving us with an open problem.