Solving steady and transient radiative transfer problems with strong inhomogeneity via a lattice Boltzmann method

Abstract

A complete lattice Boltzmann method (LBM) is developed to solve the steady and transient radiative transfer problems with strong inhomogeneity. The transient radiative transfer equation (RTE) is regarded as a hyperbolic conservation law equation and then solved by the LBM. A forward difference scheme is applied to the time derivative of the source term in the evolution equation, which makes the LBM accurate and stable for radiative transfer problems with strong inhomogeneity. The correctness and accuracy of the proposed LBM is verified first. Afterward, the LBM is applied to solve the one-dimensional radiative transfer problems involving strong inhomogeneous radiative intensity and discontinuous medium system, including a planar slab subjected to Gaussian-shaped source, an infinite slab with an inclusion layer, and a vacuum gapped medium system. The time-resolved radiation is presented and analyzed as well as the steady results. Finally, the present LBM is extended to multidimensional radiative transfer problems.