The discontinuous Galerkin method for partially ionized gas compressible flows under the influence of electromagnetic fields

摘要

The compressible Navier-Stokes equations are coupled with the full Maxwell equations through source terms encompassing the interactions and the resulting system of equations describing the flow of partially ionized gases under the influence of electromagnetic fields is solved numerically. A monoatomic partially ionized gas (Ar) is considered and additional mass conservation equations are used to evaluate the mass density of each species in the mixture electrons, ions and atoms. The coupled system is completed with a separate energy equation for electrons. The discontinuous Galerkin finite element method is used for the numerical solution and high order expansions for arbitrary-type elements are employed. For the Maxwell equations, DG discretization is performed using a divergence free vector basis 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. In order to avoid severe time step limitations imposed by the speed of light for the Maxwell system, implicit time marching is used with high order implicit Rugne-Kutta methods. Even though explicit time marching could be used for the flow the full coupled system of the Navier-Stokes and the Maxwell equations is 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. The method is applied for supersonic flows under the influence of strong magnetic fields. The effect of the electromagnetic field on partially ionized gas flow is demonstrated.