Group Invariance Method for Spherical Shock Wave in a Non-Ideal Gas under the Influence of Gravitational and Azimuthal Magnetic Fields

In the present work, we have applied the group invariance method to discuss the propagation of spherical shock wave using the concept of Roche model in a non-ideal gas under the influence of gravitational and magnetic fields for the adiabatic and isothermal flows. We have obtained the similarity solution with power law shock paths in both the ideal gas and non-ideal gas cases by the different choice of the arbitrary constant values appearing in the expression for infinitesimals. Numerical solutions are obtained for both the isothermal and adiabatic flows. The effect of the gravitational parameter, shock Cowling number, non-idealness parameter and adiabatic index on the shock strength, the density ratio across the shock front, and on the flow variables are studied. It is found that an increase in the gravitational parameter or non-idealness parameter or shock Cowling number or adiabatic index increases the density ratio across the shock front and decreases the shock strength.