Modeling and numerical simulation of propagating cylindrical shock waves under magneto-radiative fields

Abstract

In the present investigation, a mathematical model is developed to perform a comprehensive self-similar analysis of cylindrical shock wave propagation in a magnetized and radiatively absorbing medium. The governing equations of mass, momentum, energy, magnetic induction, and radiation transport are formulated by incorporating a transverse magnetic field and a generalized monochromatic absorption law. By employing an appropriate similarity transformation, the coupled magneto-radiative system is reduced to a set of five nonlinear ordinary differential equations governing the dimensionless density, velocity, pressure, magnetic field, and radiation flux. The resulting boundary-value problem is solved numerically with performing finite difference scheme. The existence and uniqueness of solutions in the vicinity of the shock front are examined, and the sonic point is identified through a regularity condition. To ensure numerical stability and convergence of the finite difference scheme, grid-independence tests are performed to confirm the accuracy and reliability of the numerical results. A comparative study between magnetized and non-magnetized cases is carried out, and the influence of the adiabatic constant on the variations of density, velocity, pressure, magnetic field, and radiation flux behind the shock front is illustrated graphically.