Finite Volume Simulation of the Compressible Orszag-Tang MGD Problem

Abstract

Computational magnetogasdynamics is an important tool to develop interdisciplinary technologies as aerospace design and for astrophysical studies. A model of a flow affected by electromagnetic forces must include the full set of Maxwell’s equations coupled with the Navier-Stokes equations (full MGD). However, in some phenomena the idea lmagnetogasdynamics equations (ideal MGD) are an accurate description. The ideal MGD equations are simplest than the full MGD equations. The ideal MGD numerical simulations allow the reduction of expensive, and sometimes unviable, experimental parametric studies. However numerical simulations are limited by the requirement of solving accurately the hyperbolic non-linear differential equations. In addition, the ideal MGD equations are nonconvex and, as consequence, the wave structure is more complex than the Euler gasdynamics equations. In this work are presented results of the compressible, twodimensional, time-dependent transient Orszag-Tang MGD problem. The results were obtained using a modification of the original finitevolume Harten-Yee TVD scheme, incorporating a new sonic fix for
the acoustic causality points.