A Curvilinear Lagrangian discontinuous Galerkin method for resistive magneto-hydrodynamics

In this paper, we present a cell-centered Lagrangian discontinuous Galerkin (DG) method for solving resistive magneto-hydrodynamics (MHD). The equations are solved using an implicit-explicit (IMEX) method. The right-hand side of the equations is classified as a hydrodynamic contribution, which is solved explicitly, and a magnetodynamic contribution which is solved implicitly. The conservative variables are discretized using Taylor basis functions within the reference element, and for magnetic field discretization, we employ a locally divergence-free basis, and it is transformed to the reference element using the Piola transformation. Nodal velocities are determined through an approximate Riemann solver. Curvilinear mesh is achieved through basis function deformation in physical space. Numerical experiments demonstrate the accuracy and robustness of the method.