The $SKN$ Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Linearly Anisotropically Scattering Plane-Parallel Medium: Part 2

The $SKN$ (Synthetic Kernel) approximation is proposed for solving radiative transfer problems in linearly anisotropically scattering homogeneous and inhomogeneous participating plane-parallel medium. The radiative integral equations for the incident energy and the radiative heat flux using synthetic kernels are reduced to a set of coupled second-order differential equations for which proper boundary conditions are established. Performance of the three quadrature sets proposed for isotropic scattering medium are further tested for linearly anisotropically scattering medium. The method and its convergence with respect to the proposed quadrature sets are explored by comparing the results of benchmark problems using the exact, $P11,$ and $S128$ solutions. The $SKN$ method yields excellent results even for low orders using appropriate quadrature set.