Finite volume simulation of 2-D and 3-D non-stationary magnetogasdynamic flow

Abstract

This work presents the development of the ideal and real magnetogasdynamic (MGD) equations in two and three spatial dimensions, followed by a modern numerical resolution method. The equations that govern the MGD flows are continuity, momentum, energy and magnetic induction together with a state equation. The method of Roe has been applied, in a high resolution Total Variation Diminishing scheme, with modifications proposed by Yee et al. For the implementation of this method in finite volumes a FORTRAN code has been developed, and it has been applied to the resolution of the magnetogasdynamic Riemann problem and the Hartman flow. Due to the high computational cost demanded by a 3D simulation, it has been necessary to reduce the grid density, compared to that used on the unidimensional and bidimensional cases. In order to evaluate this last issue, an analysis of the effect of the grid density on the results has been included at the end of the present work. The magnetogasdynamic shock tube and the Hartman flow, used as “benchmarks”, have been satisfactorily solved.