A discontinuous Galerkin method for a two dimensional reduced resistive MHD model

Abstract

We are concerned with the numerical approximation of an incompressible ionized gas (plasma) flowing in a toroidal geometry. We also assume that the flow is independent of the toroidal coordinate and the resulting model is thus 2-D. We consider a symmetric formulation, the so-called Reduced Resistive MHD model, where the governing equation gives the evolution of the axial current and vorticity (scalar variables). These equations are written in a quasi conservative form and, using the Discontinuous Galerkin (DG) framework, an approximation strategy is proposed and analyzed for triangular meshes. This approach combines a Galerkin projection of the velocity stream function and magnetic flux to obtain divergence-free approximations, together with a DG approximation of the evolutionary equations for current and vorticity, while the integration is performed using Crank–Nicholson scheme. The designed methodology is validated on the kink-mode and the tilting MHD instabilities.