Piston driven converging cylindrical shock waves in a non-ideal gas with azimuthal magnetic field

Abstract

In this article, we used the perturbation series technique to study the problem of strong converging cylindrical shock waves, collapsing at the axis of symmetry in a non-ideal gas with the effect of the azimuthal magnetic field. We assumed that the density of the undisturbed medium is uniform. With the help of the said method, we obtain a global solution to the shock implosion problem that also provides the results for Guderley’s local self-similar solution accurately, which holds merely in the neighborhood of the axis of implosion. We determined the similarity exponents and the corresponding amplitudes near the shock-collapse by expanding the shock position and flow variables in the Taylor series in t, where t is the time. Furthermore, the computed leading similarity exponents are compared with the already existing results and numerical results obtained by an alternative approach. Distributions of the gas dynamical quantities and shock trajectory are discussed through figures. The effects of variation in the non-ideal parameter (b), shock Cowling number (C0), and adiabatic index (γ) on the flow variables behind the shock and shock trajectory are also analyzed.