Numerical Methods for Two-Fluid Dispersive Fast MHD Phenomena (Communications in Computational Physics, 2011)
The finite volume wave propagation method and the finite element RungeKuttadiscontinuous Galerkin (RKDG) method are studied for applications to balancelaws describing plasma fluids. The plasma fluid equations explored are dispersive andnot dissipative. The physical dispersion introduced through the source terms leads tothe wide variety of plasma waves. The dispersive nature of the plasma fluid equationsexplored separates the work in this paper from previous publications. The linearizedEuler equations with dispersive source terms are used as a model equation system tocompare the wave propagation and RKDG methods. The numerical methods are thenstudied for applications of the full two-fluid plasma equations. The two-fluid equationsdescribe the self-consistent evolution of electron and ion fluids in the presenceof electromagnetic fields. It is found that the wave propagation method, when runat a CFL number of 1, is more accurate for equation systems that do not have disparatecharacteristic speeds. However, if the oscillation frequency is large comparedto the frequency of information propagation, source splitting in the wave propagationmethod may cause phase errors. The Runge-Kutta discontinuous Galerkin methodprovides more accurate results for problems near steady-state as well as problems withdisparate characteristic speeds when using higher spatial orders.