Numerical solution of ionized gas compressible flows under the influence of electromagnetic fields

Abstract

The compressible Navier-Stokes equations are coupled with the full Maxwell equations and the resulting system of equations describing the flow of ionized gases under the influence of electromagnetic fields is solved numerically. The discontinuous Galerkin finite element method is used for the numerical solution. High order expansions for arbitrary-type elements are employed using orthogonal and hierarchical polynomial bases for the approximation of the solution in each element. For the Maxwell equations DG discretization is performed using divergence free vector bases for the magnetic field in order to preserve zero divergence in the element and retain the global implicit constraint of a divergence free magnetic field vector down to very low levels and up to the error caused by jumps at the element interfaces. Upwind fluxes of consistent Riemann solvers are used on the elements interfaces for both the flow and the electromagnetic fluxes. In order to avoid severe time step limitations imposed by the speed of light for the Maxwell system implicit time marching is used for the full system with high order implicit Rugne-Kutta methods. It is was found that the coupled system of the Navier-Stokes and the Maxwell equations must be advance in time simultaneously to avoid wrong wave shapes and propagation speeds that are obtained when the coupling source terms are lagged in time. A fully parallelized Jacobian free Newton Krylov iterative procedure is employed with the implicit solver. Computed solutions for classical MHD problems demonstrated good agreement with existing numerical results and exact solutions. However, the present coupling approach is more general than the MHD approximation and is demonstrated for cases where the time variation of the electric field is not negligible and the MHD approximation is not valid.