Collision of characteristic shock with weak discontinuity in non-ideal magnetogasdynamics

In this paper, we consider a quasilinear hyperbolic system of partial differential equations (PDEs) governing unsteady planar or radially symmetric motion of an inviscid, perfectly conducting and non-ideal gas in which the effect of magnetic field is significant. A particular exact solution to the governing system, which exhibits space-time dependence, is derived using Lie group symmetry analysis. The evolutionary behavior of a weak discontinuity across the solution curve is discussed. Further, the evolution of a characteristic shock and the corresponding interaction with the weak discontinuity are studied. The amplitudes of the reflected wave, the transmitted wave and the jump in the shock acceleration influenced by the incident wave after interaction are evaluated. Finally, the influence of van der Waals excluded volume in the behavior of the weak discontinuity is completely characterized.