The Synthetic Kernel (SK_N) Method Applied to Thermal Radiative Transfer in Absorbing, Emitting, and Isotropically Scattering Homogeneous and Inhomogeneous Solid Spherical Medium

The $SKN$ method is proposed for solving radiative transfer problems in solid spherical participating medium. The method relies on approximating the integral transfer kernels by a sum of synthetic kernels. Then the transfer equation is reducible to a set of N-coupled second-order differential equations. The method is benchmarked against the exact and the discrete-ordinates method solutions for various optical radius and scattering albedos. Spatially varying scattering albedos are used to test the performance of the method in inhomogeneous media. Three quadrature sets are proposed for use with this method, and their convergence to the exact solution is investigated. It is demonstrated that the $SKN$ method possess the capability of solving radiative transfer problems yielding excellent solutions in solid spherical media.