Ph.D. Dissertation Defense by Scott Mosher
Monday, June 28, 2004

(Dr. Farzad Rahnema, advisor)

"A Variational Transport Theory Method for Two-Dimensional Reactor Core Calculations"


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. Significant progress has been made in re-cent years toward the goal of developing a transport method that is applicable to large, heterogeneous coarse-meshes. Unfortunately, the major 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 man-ner by considering the implications of the fission source treatment 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 func-tions was generated using orthogonal boundary conditions constructed from the discrete Legendre poly-nomials. 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 sig-nificant impact on the accuracy of the results than the type of method. The variational techniques provide better accuracy, but at substantially higher computational costs. The non-variational method is extremely robust and was shown to achieve accurate results in the 2-D problems, as long as the expansion order was not very low.