High-order lattice Boltzmann method for multi-group neutron diffusion solution

Abstract

The detailed simulation of neutron diffusion problem plays an important role in neutronics, wherein a high-order method that can be easily implemented is highly desirable, since this would likely reduce the difficulty of application of these computational techniques. In this report, a high-order lattice Boltzmann method (HLBM) is presented to solve multi-group neutron diffusion problems in both transient and eigenvalue situations. The lattice Boltzmann equation is established for the neutron diffusion problem, and the corresponding variables are determined via high-order Chapman-Enskog expansion. Both the truncation errors and the numerical results indicate that the HLBM can be used to simulate the neutron diffusion problem, with an accuracy that is much higher than that of the conventional lattice Boltzmann method. This approach may form the basis for an efficient and accurate technique for large-scale engineering, and the numerical accuracy of the proposed model can be continuously increased by adopting higher-order truncation while preserving the current level of calculation efficiency.