A three-dimensional collision probability method: Criticality and neutron flux in a hexahedron setup

In this work, the collision probability (CP) method is applied to the solution of the one-group criticality problem for a hexahedron. The method is implemented with the spatial domain being partitioned into zones, where the flat-flux approximation is used. A numerical method is employed for computing the required collision probabilities. The method is based on the subdivision of the spatial zones into elements and on the assumption that the interaction between an emission element and a collision element occurs only along the path that connects their centers of mass. The calculation is repeated, increasing the number of elements successively and using Richardson extrapolation to accelerate the convergence of the sequence of results. Some sample cases are studied in detail and a comparison with results from diffusion theory is presented.