Similarity solutions for strong shocks in an ideal gas

摘要

The method of Lie group invariance is used to obtain a class of self-similar solutions to the problem of shocks in an inhomogeneous gaseous medium and to characterize analytically the state-dependent form of the medium ahead for which the problem is invariant and admits self-similar solutions. Different cases of possible solutions, known in the literature, with a power law, exponential, or logarithmic shock paths are recovered as special cases depending on the arbitrary constants occurring in the expression for the generators of the transformation. Particular cases of plane rising shocks in an exponential medium and collapse of an imploding shock are worked out in detail. Numerical calculations have been performed to obtain the similarity exponents and the profiles of the flow variables, and comparison is made with the known results.