A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations
© 2014 The Authors. A positivity-preserving discontinuous Galerkin (DG) scheme  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  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 , 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.
Journal of Computational Physics
A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations.
Journal of Computational Physics,
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