• SIMILARITY SOLUTIONS OF SPHERICAL SHOCK WAVES IN AN IDEAL GAS WITH THERMAL RADIATION

Abstract

In this paper, a group theoretic method is used to obtain an entire class of similarity solutions to the problem of shocks propagating through in an ideal gas with thermal radiation, and to characterize analytically the state dependent form of the medium ahead for which the problem is invariant and admits similarity solutions. The arbitrary constants occurring in the expressions for the infinitesimals of the local Lie group of transformations give rise to two different cases of possible solutions i.e. with a power law and exponential shock paths. A particular case of collapse of imploding spherically symmetric shock in a medium in which the initial density obeys power law is worked out in detail. Numerical calculations have been performed to obtain the similarity exponents and the profiles of the flow variables behind the shock, and comparison is made with the Guderley’s [1] results.