A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations

A positivity-preserving discontinuous Galerkin (DG) scheme [42] is used to solve the Extended Magnetohydrodynamics (XMHD) model, which is a two-fluid model expressed with a center-of-mass formulation. We prove that DG scheme with a positivity-preserving limiter is stable for the system governed by the XMHD model or the resistive MHD model. We use the relaxation system formulation [28] for describing the XMHD model, and solve the equations using a split level implicit-explicit time advance scheme, stepping over the time step constraint imposed by the stiff source terms. The magnetic field is represented in an exact locally divergence-free form of DG [23], which greatly improves the accuracy and stability of MHD simulations. As presently constructed, the method is able to handle a wide range of density variations, solve XMHD model on MHD time scales, and provide greatly improved accuracy over a Finite Volume implementation of the same model.