Two-scale numerical solution of the electromagnetic two-fluid plasma-Maxwell equations: Shock and soliton simulation

Here, we indicate how to integrate the set of conservation equations for mass, momentum and energy for a two-fluid plasma coupled to Maxwell’s equations for the electromagnetic field, written in a composite conservative form, by means of a recently modified non-staggered version of the staggered second order central difference scheme of Nessyahu and Tadmor [H. Nessyahu, E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 408–463]. Allowing for wave propagation in one dimension, we illustrate the formation and evolution of magnetosonic shocks and solitons using two sets of time and space normalizations.