A Boundary Element - Response Matrix method for 3D neutron diffusion and transport problems

An application of a 3D Boundary Element Method (BEM) coupled with the Response Matrix (RM) technique to solve neutron diffusion and transport equations for multi-region domains is presented. The discussion is here limited to steady state problems, in which the neutrons have a wide energy spectrum, which leads to systems of several diffusion or transport equations. Moreover, the number of regions with different physical constants can be very large. The boundary integral equations concerning each region are solved via a polynomial moment expansion and the multi-fold integrals there involved are reduced to single or double integrals, taking advantage of suitable recurrence formulas. The usual unknowns (the boundary particle density and its normal derivative) are here replaced by the partial currents entering or leaving each cell. The intuitive physical meaning of such quantities facilitates the application of the response matrix technique. Only eigenvalue (criticality) problems will be here considered. As it regards the transport equation, the use of the so called Simplified Spherical Harmonics method allows, through suitable approximations, to cast the problem into a system of differential elliptic equations of the diffusion type, which can still be solved by BEM.