Analytical and numerical solution via group theoretic method for magnetogasdynamics shock wave under monochromatic radiation in non-ideal self-gravitating gas

Abstract The shock propagation in non-ideal self-gravitating gas with the azimuthal magnetic field and the monochromatic radiation effect have been investigated utilizing the Lie group theoretic method. The gas is assumed to be at rest having constant initial density and the magnetic fields in front of the shock front are assumed to be varying with time. For this problem, we obtained analytical and numerical solutions for the different classes of infinitesimal generators. The impacts of varying the strength of the magnetic field, gravitational parameter, parameter of non-idealness, and adiabatic exponent of the gas on the flow variable in the flow field region behind the shock, and on the moving shock with an exponential shock path have been studied in detail. The software package “Mathematica” has been used for numerical computation to obtain a similarity solution. It has been shown that the presence of magnetic field, non-idealness of the gas, and adiabatic exponent of the gas have decaying effect on the shock wave, but in the presence of the gravitation the shock strength is enhanced. The entire energy of the disturbance is not constant is not constant and varies with some power of the shock radius in the flow field behind the shock wave.