Similarity Solutions of Spherical Strong Shock in an Inhomogeneous Self-Gravitating Medium Using Lie Group Approach

This paper employs the similarity method to derive self-similar solutions for a model of a spherical shock wave. The discussion involves the propagation of a spherical shock wave within an ideal gas experiencing self-gravitating effects, utilizing the equation of motion and shock conditions. The expressions of infinitesimal generators within the Lie group of transformations contain arbitrary constants, leading to the identification of four potential solution cases. Among these, we focus on two cases, one following a power-law and the other an exponential law. The outcomes discussed are contingent on the variation of flow variables behind the shock, visually represented through graphical illustrations.