The SKN approximation for solving radiation transport problems in absorbing, emitting, and scattering rectangular geometries

• Published in: Journal of quantitative spectroscopy & radiative transfer 2002-04, Vol.73 (2), p.219-230
• Main Authors: Altaç, Zekeriya, Tekkalmaz, Mesut
• Format: Article
• Language: English
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/S0022-4073(01)00198-4

A high order approximation, the SK N method—a mnemonic for synthetic kernel—is introduced for solving radiation transfer problems in one- and two-dimensional geometries. The method relies on approximating the integral transport kernel by a sum of exponential kernels. The integral equation is then reducible to a set of coupled second-order differential equations— SK N equations. In this study, two types of boundary conditions have been proposed and explored. Naive boundary condition assumes one-dimensional slab boundary conditions on each boundary. Corrected boundary conditions; tackles the error terms that result from the approximation and is based on the minimization of the error term. The solutions of a test problem—incident radiation, outgoing intensities and heat fluxes at the boundaries—are compared with those of obtained by direct numerical solution of the integral transfer equation. Solutions are obtained for N=2,3,4, and 5 and are in agreement with the direct numerical solutions even for N=2 and 3. The corrected boundary condition gives better solutions than naive boundary condition in optically thin configurations; the relative errors for the intensities are below 1% while 2–4% errors are encountered in the radiation function solutions.