The coarse mesh heterogeneous response matrix method for reactor analysis.

Abstract

A heterogeneous coarse mesh scheme based on the finite element response matrix has been developed and applied to the analysis of PWR and BWR reactors. The scheme solves the diffusion equation on the assembly (or node) level, by first relating the fine mesh heterogeneous solution (i.e., flux and outgoing currents) to the input variables (i.e., source and incoming currents). This fine mesh representation takes explicitly into account the heterogeneous structure of the assembly. Contrary to many other coarse mesh methods, this scheme does not resort to any homogenization of the assembly, instead it proceeds by mapping the fine mesh representation of the solution into a coarse mesh space, through projection techniques. The mapping process is based on the residual analysis scheme which minimizes the error introduced by the source approximation in order to have consistent equations in which variables are expressed in the coarse mesh space. To solve the global problem, coupling of the neighboring nodes is necessary along with the use of a 2 layer iterative scheme. The inner iteration solves for the internal boundary conditions, and the source iteration determines the source and the system eigenvalue. To enhance the efficiency of the method, sparse matrix techniques have been used to minimize the storage space by selectively operating only on the non-zero elements of the sparse matrices. Also, a detailed power map reconstruction scheme has been added to improve the capabilities of the method. Taking advantage of the inherent parallelism of the response matrix method, a parallel algorithm has been developed in order to speed up the calculation of the parallelizable segment of the algorithm. An algorithm based on the above considerations has been successfully used to analyze BWR and PWR reactor cores. A large reduction in the storage space was observed as a result of the sparse matrix technique. Speed-ups close to theoretical predictions have been obtained with the parallel algorithm.