A time dependent two-dimensional method for the solution of the magneto-plasma dynamic coupled problem

A method for the numerical solution of the time dependent two-dimensional magneto-plasma dynamic coupled problem in the low magnetic Reynolds number case, is presented. The method is based on a time dependent two-dimensional description of the fluid dynamics iteratively coupled to a steady state two-dimensional description of the electrodynamics. This is allowed as the characteristic times of variation of the electrodynamic quantities are much lower than those of the fluid dynamic quantities. The fluid is assumed to be compressible and viscous, and governed by the Navier-Stokes equations. A semi-implicit finite difference pressure scheme has been utilised for the solution of the fluid dynamic problem. The electrodynamics is described by a second order elliptic partial differential equation obtained from the Maxwell equations and generalised Ohm's law. The elliptic equation is solved by means of an exponential fitting finite difference method. In order to test the algorithm described above, the transient of a plasma flow in a channel, caused by the variation of the externally applied magnetic field, has been studied.