Solution of the Riemann Problem in magnetogasdynamics

Abstract

In the present paper, the Riemann Problem for a quasilinear hyperbolic system of equations, governing the one dimensional unsteady flow of an inviscid and perfectly conducting gas, subjected to transverse magnetic field, is solved analytically without any restriction on the initial states. This class of equations includes, as a special case, the Euler equation of gasdynamics. The elementary wave solutions of the Riemann problem, that is, shock waves, rarefaction waves and contact discontinuities are derived and their properties are discussed. It is noticed that although the magnetogasdynamics system is more complex than the corresponding gasdynamics system, all the parallel results remain identical. It is also assessed as to how the presence of magnetic field influences the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities.