Similarity solution of spherical shock waves in the gravitational field of a variable point mass

Abstract

In this paper, we use lie group of method to study the similarity solution of spherical shock waves in the presence of gravitational field of a variable point mass. In the expressions of the generators of the local Lie group of transformations, we obtain some arbitrary constants which give rise to two cases of possible solutions such as with a power law and exponential shock paths. A particular case of the collapse of an imploding shock is discussed in detail. To obtain the similarity exponents and the flow variables, we performed numerical calculations. For the sake of comparison we also compute similarity exponent using Whitham's rule.