Current advancements in nuclear reactor core design are pushing reactor cores towards greater heterogeneity in an attempt to make nuclear power more sustainable in terms of fuel utilization and long-term disposal needs. These new designs are now being limited by the accuracy of the core simulators/methods. Increasing attention has been given to full core transport as the flux module in future core simulators. However, the current transport methods, due to their significant memory and computational time requirements, are not practical for whole core calculations. While most researchers are working on developing new acceleration and phase space parallelization techniques for the current fine mesh transport methods, this dissertation focuses on the development of a practical heterogeneous coarse mesh transport method. In this thesis, a heterogeneous coarse mesh transport method is extended from two to three dimensions in Cartesian geometry and new techniques are developed to reduce the strain on computational resources. The high efficiency of the method is achieved by decoupling the problem into a series of fixed source calculations in smaller sub-volume elements (e.g. coarse meshes). This decoupling lead to shifting the computation time to a priori calculations of response functions in unique sub-volumes in the system. Therefore, the method is well suited for large problems with repeated geometry such as those found in nuclear reactor cores. Even though the response functions can be generated with any available existing fine-mesh (deterministic or stochastic) code, a stochastic method was selected in this dissertation. Previous work in two dimensions used discrete polynomial expansions that are better suited for treating discrete variables found in pure deterministic transport methods. The amount of data needed to represent very heterogeneous problems accurately became quite large making the three dimensional extension impractical. The deterministic method was thus replaced by a stochastic response function generator making the transition to continuous variables fairly simple. This choice also improves the geometry handling capability of the coarse mesh method.

A Variational Transport Theory Method for Two-Dimensional Reactor Core Calculations Scott W. Mosher 110 Pages Directed by Dr. Farzad Rahnema It seems very likely that the next generation of reactor analysis methods will be based largely on neutron transport theory, at both the assembly and core levels. Signifi-cant progress has been made in recent years toward the goal of developing a transport method that is applicable to large, heterogeneous coarse-meshes. Unfortunately, the ma-jor obstacle hindering a more widespread application of transport theory to large-scale calculations is still the computational cost. In this dissertation, a variational heterogeneous coarse-mesh transport method has been extended from one to two-dimensional Cartesian geometry in a practical fashion. A generalization of the angular flux expansion within a coarse-mesh was developed. This allows a far more efficient class of response functions (or basis functions) to be employed within the framework of the original variational principle. New finite element equations were derived that can be used to compute the expansion coefficients for an individual coarse-mesh given the incident fluxes on the boundary. In addition, the non-variational method previously used to converge the expansion coefficients was developed in a new and more thorough manner by considering the implications of the fission source treat-ment imposed by the response expansion. The new coarse-mesh method was implemented for both one and two-dimensional (2-D) problems in the finite-difference, multigroup, discrete ordinates approximation. An efficient set of response functions was generated using orthogonal boundary conditions constructed from the discrete Legendre polynomials. Several one and two-dimensional heterogeneous light water reactor benchmark problems were studied. Relatively low-order response expansions were used to generate highly accurate results using both the variational and non-variational methods. The expansion order was found to have a far more significant impact on the accuracy of the results than the type of method. The varia-tional techniques provide better accuracy, but at substantially higher computational costs. The non-variational method is extremely robust and was shown to achieve accurate re-sults in the 2-D problems, as long as the expansion order was not very low.