Coarse-Mesh Flux-Expansion Method for the Analysis of Space-Time Effects in Large Light Water Reactor Cores

A coarse-mesh method for the solution of multidimensional neutron kinetics problems is presented that is based on the approximation of the desired solution by basis functions with local nonoverlapping supports corresponding to the volume elements of the spatial mesh. Integration of the approximating functions over their supports, and exploitation of continuity conditions for neutron flux and current, yields local seven-point difference operators with solution-dependent coupling coefficients. Due to the finite-difference (FD) structure of the resulting matrix equation, any technique developed for FD methods can be used for its solution. However, a novel (“almost implicit”) alternating direction explicit-implicit technique has been developed that is especially suited for coarse-mesh applications. Numerical examples that demonstrate the high efficiency of the method are presented. By using a spatial grid corresponding to the fuel element structure, it is possible to compute power distribution and its time history very accurately (at most, with a several percent error) at an economically tolerable expense.