An analysis of magnetogasdynamic shock wave propagation in a rotational axisymmetric self-gravitating nonideal gas

The main goal of the present study is to obtain an approximate analytical solution for a quasi-linear hyperbolic system of PDEs using the power series method. This system of PDEs pertains to the dynamics of propagation of cylindrical shock wave within a rotating axisymmetric nonideal gas. The gas, presumed to be under isothermal condition, is influenced by azimuthal magnetic and gravitational fields. The analysis incorporates variations in density, magnetic pressure, azimuthal, and axial fluid velocities according to a power law with distance from the symmetry axis in the undisturbed medium. The approximate analytical solution is obtained by expressing the flow variables as a power series. The primary focus of the study is on examining the ZOA and FOA to the solutions, including an explicit solution for the ZOA case. Figures illustrating the behavior of the flow variables behind the shock front are presented for the ZOA. Further, the investigation explores the impact of nonideal parameter, adiabatic exponent, shock Cowling number, gravitational parameter, rotational parameter and ambient density variation exponent on the flow variables.