Study of Cylindrical Magnetohydronymaic Shock Waves in Non-ideal Gas: Similarity Solution Perspective

This study endeavors to establish a similarity solution for symmetric, cylindrically converging MHD shock waves propagating into a plasma medium governed by the Mie-Gr \(\ddot{u}\) neisen equation of state (EOS). We employ the Eulerian form of the governing equations, which consider total energy and constant specific heats. Through similarity transformations, these equations are transformed into a system of Poincare-type differential equations. Subsequently, we reduce the transformed system to a finite difference set of equations, which we solve numerically using MATLAB. The research encompasses the exploration of non-ideal Royce EOS of Mie-Gr \(\ddot{u}\) neisen type, characterized by its material constants. We evaluate the similarity exponent, \(\alpha \) , and its dependence on the measure of shock strength, \(\beta \) . Notably, we observe that the shock front is influenced by the measure of shock strength, \(\beta \) , while also presenting the impact of non-idealness parameters and magnetic field strength on the flow variables.