Self-Similar Motion of Strong Converging Cylindrical and Spherical Shock Waves in Non-Ideal Stellar Medium

A theoretical model for strong converging cylindrical and spherical shock waves in non-ideal gas characterized by the equation of state (EOS) of the Mie-Gruneisen type is investigated. The governing equations of unsteady one dimensional compressible flow including monochromatic radiation in Eulerian hydrodynamics are considered. These equations are reduced to a system of ordinary differential equations (ODEs) using similarity transformations. Shock is assumed to be strong and propagating into a medium according to a power law. In the present work, two different equations of state (EOS) of Mie-Gruneisen type have been considered and the cylindrical and spherical cases are worked out in detail. The complete set of governing equations is formulated as finite difference problem and solved numerically using MATLAB. The numerical technique applied in this paper provides a global solution to the problem for the flow variables, the similarity exponent α for different Gruneisen parameters. It is observed that increase in measure of shock strength β(ρ/ρ_۰ ) has effect on the shock front. The velocity and pressure behind the shock front increases quickly in the presence of the monochromatic radiation and decreases gradually. A comparison between the results obtained for non-ideal and perfect gas in the presence of monochromatic radiation has been illustrated graphically.

Keywords:

Shock waves , Radiation hydrodynamics , Finite difference methods , Rankine , Hugoniot jump relations , Mie , Gruneisen EOS , Numerical solution