Abstract
Light propagation in three-dimensional (3D) graded index (GRIN) media has a complex spatial path, making it difficult to solve thermal radiative transfer problems. In this paper, a mesoscopic lattice Boltzmann method (LBM) that implements simple steady-state and transient radiative transfer solutions in 3D GRIN media is proposed. During the construction of the lattice Boltzmann (LB) model, the concept of the “local radiative transfer direction”, which addresses complex curved trajectories in 3D GRIN media simply, is introduced. The radiative transfer equation of 3D GRIN media can be strictly recovered from the LB model by adopting the Chapman-Enskog analysis. Numerical results indicate that radiative transfer problems in 3D GRIN media can be solved effectively by the LBM. Additionally, the influences of different optical parameters on steady-state and transient radiative transfer in 3D GRIN media are discussed. The LBM is a promising mathematical tool for radiative transfer in 3D GRIN media.
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