Neutron transport solution of lattice Boltzmann method and streaming-based block-structured adaptive mesh refinement

Simulation of neutron transport problem is the kernel of nuclear reactor physics, whose application, however, is limited by the exorbitant computational cost and complex geometry structure. This paper presents a lattice Boltzmann method (LBM) for multi-group neutron transport process and proposes a streaming-based block-structured adaptive-mesh-refinement (SSAMR) technique. The neutron lattice Boltzmann equation is deduced from the neutron transport equation and the macroscopic neutron diffusion equation can be recovered from neutron lattice Boltzmann equation via the Chapman-Enskog expansion, which makes the kinetic significance of lattice Boltzmann equation clearly. The significance of relaxation time for neutron LBM is further discussed for the first time, and the factors affecting the neutron relaxation process are studied deeply also. After establishing the neutron LBM, the SSAMR technique is applied to efficiently utilizing the computational resources of proposed LBM. To simply achieve the data communication between different meshes and eliminate the discontinuity of scalar neutron flux, a data exchange technique based on the streaming process of LBM is adopted. Simulation results show that the proposed LBM can be applied to solving neutron transport process in all dimensions, and the SSAMR technique can not only effectively reduce the computational cost, but also be easily implemented. This work may provide some new perspectives for solving the neutron transport process and a powerful thought for large and complex engineering calculation.