Evolution of weak shock waves in non-ideal magnetogasdynamics

In this article, a study concerning the growth and decay of weak shock waves in non-ideal magnetogasdynamic regime has been performed. One-dimensional plane and cylindrical symmetries are assumed. The flow medium is considered as a perfectly conducting non-ideal gas permeated with either axial or azimuthal magnetic field. The Generalized Wavefront Expansion (GWE) method used in this work provides a system of coupled non-linear transport equations which completely describe the evolution of weak shocks and first order discontinuities induced behind it. The solution obtained during the process agrees with the classical decay laws for weak shocks. A general criterion for steepening of compressive waves and flattening of expansion waves has been derived. Further, the effect of geometrical spreading, magnetic field, and non-idealness of the gas on steepening or flattening of waves is discussed and illustrated via figures. Also, a comparison between growth and decay of weak shocks in ideal and non-ideal magnetogasdynamic regimes has been made. It has been observed during the study that all compressive waves evolve into shock regardless of their initial strength, and expansive waves decay and damp out eventually.