Fully-implicit finite volume method for the ideal two-fluid plasma model

We present a novel numerical model that simulates ideal two-fluid plasmas coupled to the full set of Maxwell's equations with application to space and laboratory plasmas. We use a fully-implicit finite volume method for unstructured meshes, that uses an advection upstream splitting method (i.e., AUSM+-up) for all speeds to discretize the numerical fluxes of the fluids. In addition, we discretize Maxwell's equations with a modified-Rusanov scheme. The electromagnetic numerical dissipation is scaled using the scales of the fluid-electromagnetics coupled problem that are found to be very different from those of the uncoupled problem. Our numerical scheme guarantees that the elliptical constraints of Maxwell's equations are satisfied by using hyperbolic divergence cleaning. We validate the performance and accuracy of our model by simulating the following conventional cases: a circularly polarized wave, a Brio-Wu type shock tube, and a two-fluid plasma reconnection with the GEM challenge set up. Our model reveals the complexity of the two-fluid model compared to magnetohydrodynamics (MHD) models, as the inclusion of charge separation, the displacement current and the electron dynamics present are ignored by the MHD simplifications. The two-fluid model shows the presence of electromagnetic and plasma waves and the effect that they have in even the simplest cases. We also compare our model to other available two-fluid models and find our results to be in good agreement.