Simulating Magnetohydrodynamic Instabilities with Conservative Perturbed MHD Model Using Discontinuous Galerkin Method (Communications in Computational Physics, 2018)
In magnetically confined plasma research, the understandings of small andlarge perturbations at equilibrium are both critical for plasma controlling and steadystate operation. Numerical simulations using original MHD model can hardly giveclear picture for small perturbations, while non-conservative perturbed MHD modelmay break conservation law, and give unphysical results when perturbations growlarge after long-time computation. In this paper, we present a nonlinear conservativeperturbed MHD model by splitting primary variables in original MHD equations intoequilibrium part and perturbed part, and apply an approach in the framework of discontinuousGalerkin (DG) spatial discretization for numerical solutions. This enableshigh resolution of very small perturbations, and also gives satisfactory non-smoothsolutions for large perturbations, which are both broadly concerned in magneticallyconfined plasma research. Numerical examples demonstrate satisfactory performanceof the proposed model clearly. For small perturbations, the results have higher resolutioncomparing with the original MHD model; for large perturbations, the non-smoothsolutions match well with existing references, confirming reliability of the model forinstability investigations in magnetically confined plasma numerical research.