An analytical solution for the consideration of the effect of adjacent fuel elements

A new analytical method is described to deal with the Leakage Environmental Effect – the influence of the adjacent fuel element on the cross section preparation. The method is discussed and classified in comparison with other methods given in the literature. The new method is based on the analytical solution of the two group diffusion equation for two adjacent fuel elements. The specifics needed to create a highly efficient analytical solution are discussed. The very promising quality of the results for this highly efficient method is demonstrated on a homogeneous test case and on several heterogeneous combinations of two fuel elements described in the PWR MOX/UO2 CORE TRANSIENT BENCHMARK. One important advantage is the unproblematic extension of the solution to two-dimensional problems, since the analytical solution for each fuel element will be of the identical structure. Only the filled in data for the four fuel element quarters will vary. The coupling of the fuel elements does not affect the exponential solutions, only the constants attached to the single exponentials. Thus, the coupling will be solved in a system of linear equations.