SIMILARITY SOLUTIONS FOR CONVERGING SHOCKS IN A RELAXING GAS

In the present paper, we use the method of Lie group invariance to det ermine the class of self-similar solutions to a problem concerning pla ne and radially symmetric flows of a relaxing gas involving shocks of arbitrary strength. The ambient gas ahead of the shock is considered t o 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 loc al Lie group of transformations, give rise to different cases of possi ble solutions with a power law, exponential or logarithmic shock paths . In contrast to situations without relaxation, the inclusion of relax ation effects imply constraint conditions. A particular case of the co llapse of an imploding shock is worked out in detail for radially symm etric flows. Numerical calculations have been performed to determine t he effects of relaxation and the ambient density on the self-similar e xponent and the flow patterns.