SUMMARY

Many reactor analysis methods include spatial homogenization of assemblies or pin cells to reduce the complexity of the problem. In order to preserve the reaction rates, the homogenized cross sections are defined as the flux weighted average of the heterogeneous cross sections over the homogenized region. In diffusion theory if the heterogeneous transport solution is known a priori, consistent homogenization and de-homogenization techniques are available to reconstruct the heterogeneous solution with the correct choice of homogenized cross sections and discontinuity factors. Different methods have been introduced to take into account the core environment in lattice calculations when the heterogeneous solution is not known. Among these methods the high-order homogenization method is consistently accurate regardless of the degree of the heterogeneity of the fuel assembly or the reactor core. In transport theory, a systematic homogenization theory and a self-consistent de-homogenization theory for fuel assemblies have been developed using a multiple-scales asymptotic expansion method. This method was developed for eigenvalue problems associated with the one-group neutron transport equation for a large three-dimensional heterogeneous system comprised of a two-dimensional array of near-periodic fuel assemblies. This thesis focuses on a new method for spatial homogenization in transport theory that is based on the concept of discontinuity factors and a source correction term expanded in orthogonal basis.