SIMILARITY SOLUTIONS FOR CONVERGING SHOCKS IN A RELAXING GAS

In the present paper, we use the method of Lie group invariance to determine the class of self-similar solutions to a problem concerning plane and radially symmetric flows of a relaxing gas involving shocks of arbitrary strength. The ambient gas ahead of the shock is considered to be inhomogeneous. The method yields a general form of the relaxation rate for which the self-similar solutions are admitted. The arbitrary constants, occurring in the expressions for the generators of the local Lie group of transformations, give rise to different cases of possible solutions with a power law, exponential or logarithmic shock paths. In contrast to situations without relaxation, the inclusion of relaxation effects imply constraint conditions. A particular case of the collapse of an imploding shock is worked out in detail for radially symmetric flows. Numerical calculations have been performed to determine the effects of relaxation and the ambient density on the self-similar exponent and the flow patterns.