Exact homogenization scheme for the S/sub n/ equations
Hassan A. Khalil · Transactions of the American Nuclear Society · 1985
In the application of nodal methods to the solution of the transport and diffusion equations, systematic and accurate procedures for computing homogenized nodal parameters are needed. For the diffusion equation, a formally exact homogenization approach has been developed for Koebke. With this approach, the knowledge of a high-order solution for a heterogeneous problem can be used to deduce node boundary scalar flux discontinuities whose use in a homogenized (low-order) calculation enables this calculation to reproduce, in an integral sense, the heterogeneous solution. Thus these flux discontinuities, referred to as discontinuity factors, not only account for heterogeneities, but also compensate for any additional approximations made in the low-order scheme. In practice, when the high-order solution is not known a priori, the discontinuity factors (DF) must be approximated. Methods of estimating the DF for the diffusion equation have been devised. However, as can be expected the difficulty and expense of obtaining adequate approximations of the DF increase as the difference between the low-order and high-order schemes increases. Thus even though high-order transport effects can be reproduced by solving the diffusion equation using DF, the use of an S/sub n/ method as the low-order scheme is expected to be more effective for manymore » problems. For this reason, Koebke's exact homogenization theory for the diffusion equation is extended to the S/sub n/ equations in this summary.« less