Propagation of shock waves in a non-ideal gas with dust particles in an interstellar medium

The present paper demonstrates the study of propagation of converging shock waves in a spherical interstellar cloud of an non-ideal gas (van der Waals type) with dust particles using group theoretic technique. The Lie group of transformation is used to determine the whole range of similarity solutions to a consider problem of spherically symmetric flows in an non-ideal gas with dust particles in an interstellar medium involving strong converging shocks. Group theoretic technique brings the different possible cases of potential solutions considering different cases for the arbitrary constants appearing in the expressions of infinitesimals of the Lie group of transformation. Numerical solutions are obtained in the case of power law shock path. The collapse of an imploding shock for the spherically symmetric flow with power law shock path is worked out in detail. The similarity exponents are estimated numerically for the different values of van der Waals excluded volume, dust parameters, and the values of leading similarity exponents are compared with the results obtained from the Chester-Chisnell-Whitham approximation (CCW approximation). The effects of relative specific heat, van der Waals excluded volume, mass fraction of dust particles and ratio of density of dust particle to the density of gas have been shown on the flow variables. The distribution of the flow variables in the flow-field region behind the shock is shown in graphs.