A discontinuous Galerkin method for a two dimensional reduced resistive MHD model. (15th August 2019) - Chandrashekar, Praveen
Highlights: Discontinuous Galerkin method developed for symmetric form of reduced MHD equations. Current and vorticity are evolved dynamically with DG scheme. Continuous Galerkin method is used for the elliptic components. Stable schemes without any tunable parameters are obtained using Crank–Nicholson scheme in time. Application to tilt instability and current hole problem confirms validity of the approach. 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.