Lattice Boltzmann method for solving non-equilibrium radiative transport problems

Recently developed lattice Boltzmann equation (LBE) framework (Bindra et al., 2012; McCulloch and Bindra, 2016) for radiation transport is extended to solve time-dependent non-equilibrium radiative and neutron transport problems. Dynamics of radiation and material energy exchange is modeled by coupling radiation transport equation with the material energy equation in a one-dimensional isotropically scattering homogenous medium. The LBE solutions are compared against the existing semi-analytical P1 benchmark and show good agreement for different times. Furthermore, a two-dimensional D2Q8 lattice Boltzmann method is proposed for solving the neutron transport equation in a heterogenous media (e.g., 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.