Finite volume methods for the two-fluid MHD equations

Two fluid (TF) ideal magnetohydrodynamics (MHD) equations are a generalized form of the ideal MHD equations in which the electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of the non-linearities and the presence of stiff source terms, particularly for realistic charge to mass ratios. We design novel finite volume schemes based on an implicit-explicit (IMEX) time stepping routine. The special structure of the twofluid MHD equations enable us to split the source terms carefully in order to ensure that only local (in each cell) equations need to be solved at each time step. Furthermore, these equations are solved exactly. Benchmark numerical experiments are presented to illustrate the efficiency of new approach.