Converging strong shock wave from a cylindrical piston in a Van der Waals magnetogasdynamics with dust particles

Abstract

In this study, by using the perturbation series approach, a global solution to the implosion problem is obtained for a quasi-linear hyperbolic system of partial differential equations (PDEs) describing a problem of strong converging cylindrical shock waves collapsing at the axis of symmetry in a Van der Waals dusty gas under the effect of axial magnetic field. This global solution provides the results of Guderley’s local self-similar solution which is valid only in the neighborhood of the axis of implosion. The similarity exponents and corresponding amplitudes are obtained in the neighborhood of the shock collapse. In addition, the values of leading similarity exponents are compared with the results obtained by Whitham’s method. The shock trajectory and flow variables (i.e., density, velocity, pressure and magnetic pressure) have been drawn for different values of the relative specific heat, the mass concentration of dust particles, the ratio of the density of solid particles to the initial density of the gas, Van der Waals excluded volume and shock Cowling number.