A resistive extension for ideal magnetohydrodynamics

We present an extension to the special relativistic, ideal magnetohydrodynamic (MHD) equations, designed to capture effects due to resistivity. The extension takes the simple form of an additional source term that, 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 principles 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.