Similarity Solutions for Imploding Shocks in a Non-ideal Magnetogasdynamics

In the present paper, we use a Lie group of transformations to obtain a class of similarity solutions to a problem of a cylindrically symmetric shock wave propagating through one-dimensional, unsteady flow of a non-ideal gas. We assume that the gas has infinite electrical conductivity under the influence of axial component of the magnetic field, with isothermal flow condition. The density of the ambient medium is taken to be uniform ahead of the shock. The generators of the Lie group of transformations involve arbitrary constants which yield two different cases of possible solutions with a power law shock path and exponential shock path. We present a detailed investigation for the case of power law shock path. Numerical computations have been carried out to find out the flow patterns in the flow-field behind the shock and the values of similarity exponent. Further, we compare the obtained similarity exponent with that obtained by Guderley’s (Luftfahrtforschung 19:302–312, 1942) method. The effects of the non-ideal parameter and magnetic field strength on the similarity exponent and the flow patterns have also been studied. All computations have been done using the software package MATHEMATICA. © 2020, Springer Nature India Private Limited.