Verification and validation of the maximum entropy method of moment reconstruction of energy dependent neutron flux

The method of moments in conjunction with the maximum entropy method of reconstructing density distributions is applied to the energy dependent neutron diffusion equation to solve for neutron flux within a critical assembly. The energy dependent neutron diffusion equation (EDNDE) is converted into a moment equation which is solved analytically for a bare spherical critical assembly of pure 235U in the radial direction. The normalized energy dependent neutron diffusion moments (NEDNDM) generated analytically is verified to NEDNDM, as calculated by Monte Carlo N Particle 5 version 1.40 (MCNP5) and Attila-7.1.0-beta version (Attila). The normalized NEDNDM are validated with the bare spherical critical assembly experiment, named GODIVA. The NEDNDM are then put into the maximum entropy method to solve for neutron flux within the two critical assemblies (100% 235U and GODIVA) and the neutron flux is verified with MCNP5 and Attila and validated with GODIVA. The analytic NEDNDM values fall between the NEDNDM from MCNP5 (lower bound) and Attila (upper bound). The error is taken to be relative to the Monte Carlo simulation. The error range is from 0% to 14%. The error range of the NEDNDM compared to NEDNDM from GODIVA is 0% to 24%. The verification and validation error of the maximum entropy method is 12% to 25% where MCNP5 is taken to be the comparison standard. The error range of the reconstructed flux validated with GODIVA is 0% to 10%. The error range of the neutron flux spectrum from MCNP5 compared to GODIVA is 0%-20% and the Attila error range compared to the GODIVA is 0%-35%. The method of moments coupled with the maximum entropy method for reconstructing flux is shown to be a fast reliable method, compared to either Monte Carlo methods (MCNP5) or 30 multienergy group methods (Attila) and to GODIVA the bare sphere critical assembly experiment.