A discontinuous Galerkin method for two-temperature plasmas

We develop a formulation for the single-fluid/two-temperature equations for simulating two-species, compressible, non-equilibrium plasma flows. The divergence-free condition of the magnetic field is enforced via the characteristic decomposition of an extended nine-wave system. The source terms are modified appropriately to improve energy and momentum conservation accuracy. A spectral/hp element algorithm is employed in the discretization combined with a discontinuous Galerkin formulation for the advective and diffusive contributions. The formulation is conservative, and monotonicity is enforced by appropriately lowering the spectral order around discontinuities. A new MHD flux introduced here is the MHD-HLLC (Harten–Lax–van Leer Contact wave) flux that preserves monotonicity and resolves contact discontinuities better. Exponential convergence is demonstrated for a magneto-hydrostatic problem. Two tests are presented using the new MHD-HLLC flux. Also, the differences between the single-temperature and the two-temperature models are presented for two-dimensional plasma flows around bluff bodies.