Akmal Husain

An Approximate Analytical Solution of Imploding Strong Shocks in a Non-Ideal Gas through Lie Group Analysis

The method of Lie group transformation is used to obtain an approximate analytical solution to the system of first-order quasilinear partial differential equations that govern a one-dimensional unsteady planer, cylindrically symmetric and spherically symmetric motion in a non-ideal gas, involving strong shock waves. Invariance groups admitted by the governing system of partial differential equations, which are indeed continuous group of transformations under which the system of partial differential equations remains invariant, are determined, and the complete Lie algebra of infinitesimal symmetries is established. The infinitesimal generators are used to construct the similarity variables. These similarity variables are used to reduce the governing system of partial differential equations into a system of ordinary differential equations.

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

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.