Anti-symmetric representation of the extended magnetohydrodynamic equations

Abstract

We introduce the anti-symmetric representation of the extended magnetohydrodynamic (MHD) equations. In this representation, the use of the anti-symmetric flux operator (∇·v+v·∇) results in conservation theorems with discrete analogs. Inherently robust numerical applications are achieved with little effort, and conservation to machine precision is possible with simple numerical schemes. Starting from the two-fluid equations, we construct a single-fluid MHD model based on generalized center-of-mass variables for the mass (ρ), momentum (ρv), and pressure (p). This model is shown to possess identical conservation properties to the two-fluid system, with the only restriction being the use of a single temperature. Common approximations to the Braginskii heat fluxes and to the gyroviscous stress tensor are cast into our representation for convenience. The discrete conservation properties are verified using the classic Orszag–Tang vortex problem. In addition to the favorable mass, momentum, and energy conservation properties, the time reversibility of the simulations is demonstrated.