A resistive extension for ideal MHD

Abstract

We present an extension to the special relativistic, ideal magnetohydrodynamics (MHD) equations, designed to capture effects due to resistivity. The extension takes the simple form of an additional source term which, when implemented numerically, is shown to emulate the behaviour produced by a fully resistive MHD description for a range of initial data. The extension is developed from first principle arguments, and thus requires no fine tuning of parameters, meaning it can be applied to a wide range of dynamical systems. Furthermore, our extension does not suffer from the same stiffness issues arising in resistive MHD, and thus can be evolved quickly using explicit methods, with performance benefits of roughly an order of magnitude compared to current methods.