Similarity Solutions of Cylindrical Strong Shock in Self-Gravitating Medium Under the Monocromatic Radiation

A class of self-similar solutions to the model of a cylindrical shock wave in non-uniform atmosphere in the presence of monochromatic radiation and gravitation in magneto gas dynamics has been obtained by using a similarity method. The propagation of a cylindrical shock wave in an ideal gas with monochromatic radiation and gravitating effects has been discussed. Through applying similarity transformations to the system of equations, we obtained the symmetry generators of the system. By using the symmetry generators and the surface invariance condition, we obtained the group invariant solution and then, with the help of group invariant solution, we converted the given system of PDEs to the system of ODEs together with the boundary condition. The obtained system of ODEs together with boundary condition has been solved numerically by using Runge–Kutta method of order four. The flow variables are analyzed graphically behind the shock with respect to the variation of parameters.