A perturbation approach to study the shock wave propagation in a non-ideal magnetogasdynamics under isothermal condition

Abstract

The main goal of this paper is to obtain a global solution to the problem of imploding strong cylindrical shock waves (SWs) collapsing at the axis of symmetry in a non-ideal gas under the influence of an axial magnetic field using the perturbation series technique. This global solution is valid for the entire flow field up to the instant of collapse. Guderley's asymptotic solution, which is only applicable in the neighborhood of the axis of implosion, is properly reproduced by this global solution. Guderley's local self-similar solution allows for the determination of the first dominant similarity exponent only; however, this approach also enables the identification of additional, less dominant similarity exponents along with the corresponding amplitudes. Additionally, the computed values of the similarity exponents have been compared with the results drawn from Guderley's approach. The profiles of fluid variables and shock trajectory are shown graphically for different values of the non-ideal parameter, adiabatic index, and shock Cowling number. The “Mathematica” software has been used to do all numerical computations.