Asymptotic Freedom in the Diffusive Regime of Neutron Transport

The accuracy of a numerical method for solving the neutron transport equation is limited by the smallest mean free path in the problem. Since problems in the asymptotic diffusive regimes have vanishingly small mean free paths, it seems hopeless, given a limited amount of computer memory, that an accurate solution can be obtained for these problems. However we found that the accuracy of a numerical method improves as the scattering ratio increases with the total cross section and the grid spacing held fixed for problems that are in the asymptotic diffusive regime. This phenomenon is independent of the numerical method and can be explained on physical grounds. The numerical results by the Diamond Difference Method are given to show this phenomenon