Converging shock wave in Darcy-type porous medium through nonstandard analysis

Abstract

A problem of propagation of strong plane and converging shock wave is studied in unsteady, Darcy-type porous media. Nonstandard analysis is used to derive the jump conditions for both plane and converging shock waves. It is also assumed that the shock thickness occurs at innitesimal interval and jump functions in low parameters are smooth across this interval. The distribution of low parameters across the shock wave are expressed in terms of Heaviside functions and Dirac Delta measures. Numerical computations have been performed to study the eect of porosity of the medium on the distribution of the ow parameters.