Lattice Boltzmann Method for Solving Time-Dependent Radiation Transport and Reactor Criticality Problems

The recently developed lattice Boltzmann equation (LBE) framework [1] for radiation transport is extended to solve time-dependent nonequilibrium neutron transport problems. Dynamics of radiation and material energy exchange is modeled by coupling the radiation transport equation with the material energy equation in a one-dimensional isotropically scattering homogenous medium. The LBE equations are obtained for corresponding radiative or neutron transport in constant source and reactor criticality search problems. Furthermore, a two-dimensional D₂Q₈ & D₂Q₁₆ LBEs are proposed for solving the time-dependent neutron transport equation in a heterogenous media (e.g., a checkerboard lattice with pure scattering and absorbing cells). The results obtained with LBE are in good agreement with the existing discrete ordinate method results for the benchmark problem.