A 3D Lattice Boltzmann method for light simulation in participating media

In recent years, Lattice Boltzmann methods (LBM) have been extended to solve the radiative transport equation (RTE), which describes radiative transport through absorbing and scattering media. With the present work, a new approach for solving RTE by LBM, referred to as RTLBM, is proposed for D3Q7 grids. Its derivation is strongly linked to the P1-method, which approximates the RTE by a macroscopic diffusion equation with an additional sink term. For the fist time, a comprehensive evaluation of an RTLBM is shown. First of all, it is shown by a Chapman-Enskog expansion, that the proposed RTLB equation solves the corresponding macroscopic target diffusion equation with additional sink term. Based on corresponding analytical solutions, a stringent and extensive numerical error analysis, with focus on grid convergence and grid independence, is presented. An experimental order of convergence of two is observed solving the steady-state diffusion equation with additional sink term.