Lie group transformation method for shock wave in rotating non-ideal gas with or without magnetic field, and interaction of characteristic shock with weak discontinuity

Abstract

An analytical solution for power-law shock paths and a numerical solution for exponential-law shock paths to the system of equations that describes a cylindrical shock wave in a rotating non-ideal gas with or without an axial magnetic field is determined by utilizing the Lie group invariance method. In an undisturbed medium, the axial magnetic field and azimuthal fluid velocity are meant to be variable; however, the density is taken to be constant. The liberty to choose the value of arbitrary constants that are in the equation for an infinitesimal generator gives rise to three different cases, i.e., the power law, a particular case of the power law, and the exponential-law shock paths. In the power-law case, a particular solution in an analytical form is obtained, while for an exponential-law case, a numerical solution is obtained. By considering this analytical solution, the development of the characteristic shock and its interaction with a weak discontinuity are also discussed. The effects of the rotational and non-idealness parameters on the characteristic shock and on the acceleration wave's amplitude are discussed. The expressions for the jump in shock acceleration and the amplitude of the transmitted and reflected wave are obtained.