Nonstandard analysis of a converging shock wave in a nonideal gas

Abstract

The problem of propagation of strong plane and converging shock waves in an unsteady inviscid nonideal gas is studied. A nonstandard analysis is used to derive the jump conditions for both shock waves. It is assumed that the jump occurs on an infinitesimal interval and jump functions in the flow parameters are smooth across this interval. The distribution of the flow parameters across the shock wave is expressed in terms of the Heaviside functions. Numerical computation to study the distribution of the flow parameters is performed. © 2011 Springer Science+Business Media, Inc.