The SKN Approximation for Solving Radiation Transport Problems in Absorbing, Emitting, and Scattering Media

Authors: Zekeriya ALTAÇ

Abstract: A high order approximation, the SK_N method, a mnemonic for synthetic kernel, is introduced for solving radiation transfer problems. The method relies on approximating the integral transport kernels by a sum of diffusion-like kernels. The integral equation is then equivalent to a set of coupled second-order differential equations for which proper boundary conditions can be established. The method is tested for a combined conduction and radiation problem between infinitely long gray plates in an absorbing, emitting and scattering medium. The problem is solved by the direct numerical solution of the integral equation and compared to that of SK_N approximation. The results are, for N>=3, in excellent agreement with the direct numerical solutions. Depending upon the error tolerances in practical problems, SK_2 approximation may, as well, be used.

Keywords: Radiative transfer, participating medium, scattering medium, SK_N method