Optimal classification of Lie-subalgebras and similarity solution for shock wave in a self-gravitating rotating non-ideal gas with magnetic field: isothermal flow

Abstract We have used the Lie group analysis technique to investigate all possible similarity solutions for 1-D unsteady isothermal flow behind a shock wave in a self-gravitating rotating non-ideal gas with axial or azimuthal magnetic field. For the system of basic equations, the optimal system is computed based on one-dimensional Lie sub algebras. After obtaining the optimal system of solvable Lie sub algebras, all possible similarity solutions of the considered problem are obtained first time. With the aid of optimal classes, we obtained the similarity variable and the similarity transformation that transform the system of partial differential equations into a system of ordinary differential equations. It is observed that an increase in the magnetic field strength, non-idealness parameter, rotational parameter, and adiabatic index has a decaying effect on the shock wave strength. On changing the azimuthal to axial magnetic field or by increasing the gravitational parameter, the shock wave strength increases.