Similarity solutions for strong shock waves in magnetogasdynamics under a gravitational field

In the present paper, we use a Lie group of transformations to obtain a class of similarity solutions to a problem of cylindrically symmetric strong shock waves propagating through one-dimensional, unsteady, and isothermal flow of a self-gravitating ideal gas under the influence of azimuthal magnetic field. The density of the ambient medium is assumed to be non-uniform ahead of the shock. The generators of the Lie group of transformations involve arbitrary constants which yield four different cases of possible solutions. Out of all possibilities, only two cases hold similarity solutions. One is with a power law shock path, and the other one is with an exponential law shock path. We present a detailed investigation for the case of power law shock path. Numerical computations have been performed to find out the flow patterns in the flow-field behind the shock. Also, we have analyzed the effects of variation in adiabatic index, ambient density exponent, gravitational parameter, and Alfven-Mach number on the flow variables behind the shock. All computations have been done using the software package MATLAB.