The Incident Flux Response Expansion Method for Heterogeneous Coarse Mesh Transport Problems

A generalization of the response expansion previously used to develop a variational heterogeneous coarse mesh transport method has been accomplished. This allows a broad class of response functions to be employed within the framework of the original variational principle. New finite element equations were derived based on the general expansion, along with an additional assumption that seemingly breaks the tight coupling that created numerical difficulties in previous work. In addition, the nonvariational method was developed in a new and more thorough manner by considering the implications of the fission source treatment imposed by the response expansion. Results are presented for several heterogeneous light water reactor benchmark problems in the one‐dimensional, multigroup, discrete ordinates approximation. An efficient set of response functions was constructed using the discrete Legendre polynomials as boundary conditions. It was found that the expansion could be truncated at a low order without a significant loss of accuracy. In addition, the expansion order was found to have a much greater impact on the results than the type of method.

Keywords:

• Transport theory
• Reactor physics
• Coarse mesh method
• Interface model
• Flux expansion
• Discrete legerdre polynomial

Acknowledgments

The authors gratefully acknowledge the support of this work by the U.S. Department of Energy's Nuclear Energy Research Initiative (NERI) under contract number DE‐FG03‐02SF22619, NERI Grant 2002‐81.