Piston driven converging shock waves in nonideal magnetogasdynamics of variable density

Abstract

In this article, we analyze an imploding strong shock wave problem collapsing at the axis of cylindrical piston filled with a nonideal gas of nonuniform density that is decreasing toward the axis of symmetry according to a power law. The magnetic field is considered to be present in the axial direction, and the electrical resistance is assumed to be zero. The perturbation series technique applied to the system of hyperbolic partial differential equations governing the one-dimensional adiabatic cylindrically symmetric flow of a nonideal gas in the presence of an axial magnetic field provides us a global solution and also recovers Guderley's local solution, which holds only in the neighborhood of shock collapse. All possible similarity exponents and corresponding amplitudes are found by expanding all the flow variables and shock location in powers of time. A comparison has been made between the computed values of similarity exponents with published results in the literature, and the results are in good agreement. The flow parameters and shock position have been analyzed graphically.