Landau—Stanyukovich Rule and the Similarity Parameter of Converging Shock Waves in Magnetogasdynamics

Abstract

Second-kind self-similar solutions to a problem of converging cylindrical shock waves in magnetogasdynamics are investigated. Two trial functions suggested by Chisnell and the shooting method of Landau—Stanyukovich are used to determine the similarity exponent for different values of specific heat ratio γ and the parameter k, where k ∊ (0, 1]. Detailed analyses of flow patterns for different values of adiabatic heat exponent and magnetic field strength are carried out. It is observed that the general behavior of the velocity and density profiles is not affected in a magnetogasdynamics regime whereas there is an increase in the absolute value of the flow parameters with an increase in the magnetic field strength. However, the pressure profiles are greatly affected by the magnetic field interaction.