Convergence of strong shock waves in non-ideal magnetogasdynamics

Abstract

The problem of a strong cylindrical shock wave collapsing at the axis of symmetry is studied in non-ideal magnetogasdynamics. The perturbation approach used in this work provides a global solution to the shock implosion problem in non-ideal magnetogasdynamics in contrast to Guderley’s asymptotic solution that holds in the vicinity of the axis of implosion. We analyze the flow parameters by expanding the solution in powers of time and found the similarity exponents as well as the corresponding amplitudes in the vicinity of the shock-collapse. Along with the higher-order terms in Guderley’s asymptotic solution, the leading similarity exponents have been refined near the center of convergence. The flow parameters and the shock trajectory have been drawn in the region extending from the piston to the center of collapse for different values of the adiabatic coefficient, shock cowling number, and non-ideal parameter.