Verification of Method of Moments Approach to the Solution of the Neutron Transport Equation

Quadrature method of moments (QMOM) is to be applied to the neutron transport equation within multi-physics computational fluid dynamics (CFD) simulations of nuclear fuel processing units to assess nuclear safety issues in the design of various unit operations. Before this can be done, it is necessary to verify that the method of moments provides accurate solutions to the neutron transport equation formulated as the neutron diffusion equation for various simple geometries, neutron energies and neutron fluxes. In this paper, the neutron transport equation is solved both analytically and numerically using the industrial standard software MCNP for various geometries and compared with analytical solutions to the moment-based neutron diffusion equation. These results show that the method of moments is an accurate representation of the solution to the neutron diffusion equation and that 3 to 5 moments is all that are needed to represent the neutron population even when it is bimodal in neutron energy.