On the simulation of neutron noise using a discrete ordinates method

Abstract

The method of discrete ordinates is investigated for neutron noise simulations in the frequency domain. For this purpose, the solver NOISE-SN is developed and used to simulate two neutron noise problems that are respectively derived from the two-dimensional systems described in the neutron transport simulation benchmarks C4V and C5G7. In the first problem based on the C4V system, NOISE-SN is compared to the diffusion-based simulator CORE SIM+. These results show that NOISE-SN and CORE SIM+ calculate similar spatial distributions of neutron noise, although significant differences can be found at the location of the perturbation and at locations with strong variations of material properties, where the discrete ordinates method is expected to be more accurate than diffusion theory. Then NOISE-SN calculations are performed to test different SN approximations, and the fictitious source method that may be applied to mitigate possible numerical artifacts, known as the ray effect. In the second problem based on the C5G7 system, the choice of a low order of discrete ordinates in NOISE-SN leads to unphysical values of the neutron noise because of the ray effect. The increase of the order of discrete ordinates or introducing a fictitious source in the equations to be solved alleviates the issue. The second option is shown to remove the ray effect without a high order of discrete ordinates and thus without too expensive calculations, even though the strength of the fictitious source needs to be tuned carefully to avoid very slow convergence rates.