Studies of Plasma Instabilities using Unstructured Discontinuous Galerkin Method with the Two-Fluid Plasma Model

The discontinuous Galerkin (DG) method has the advantage of resolving shocks and sharp gradients that occur in neutral fluids and plasmas. An unstructured DG code has been developed in this work to study plasma instabilities using the two-fluid plasma model. Unstructured meshes are known to produce small and randomized grid errors compared to traditional structured meshes. Positivity and monotonicity limiters that retain high order in the solution are not trivial for the two-fluid plasma model due to the presence of physical plasma dispersions. Some discussion on the limiters will be presented. Richtmyer Meshkov instabilities are studied in an expansion wave test performed in a periodic rectangular domain using MHD model and two-fluid plasma model. Simulations of Kelvin-Helmholtz instabilities using two-fluid plasma model are performed. Computational tests for Rayleigh-Taylor instabilities in radially-converging flows are performed using the MHD model and two-fluid plasma model. Choice of grid geometry is not obvious for simulations of instabilities in these circular configurations. Comparisons of the effects for different grids are made.