Symmetries Applied to Reactor Calculations

Solving problems of reactor physics is well developed for typical pressurized water and boiling water reactor geometries but less developed for high-temperature gas-cooled reactor, liquid-metal fast breeder reactor, and WWER (BBP) geometries. Several problems of reactor physics can be formulated in a geometry-independent fashion with the help of symmetry considerations, which allows the solution to be decomposed into eigenfunctions of the symmetry operations. An analytic coarse-mesh solution is derived without resorting to the cross leakage concept. The method is applicable to arbitrary geometries. A second-stage homogenization based on the Bloch theorem is presented. It is shown that the solution of the transport equation can always be made up from a cell problem set (microfunctions) and from an overall solution to the diffusion equation (macrofunction).