Spectral simulation of light propagation in participating media by using a lattice Boltzmann method for photons

A lattice Boltzmann method for radiation transfer and Newton-Cotes formulas are used in this work to compute the propagation of polychromatic light in a biosuspension of phototrophic microorganisms. The polychromatic light field is obtained from monochromatic lattice Boltzmann simulations by integration across the visible spectrum. The effects of the spectral resolution, radiation characteristics and the chosen integration rule on the accuracy of the integration are investigated. It was found that reasonable results can be achieved on equidistant spectral grids with a grid spacing of Δλ ≤ 20 nm, although error compensation might be a serious issue if the trapezoidal rule is applied. Based on a priori information about the light field, an approach for the computation of adapted spectral grids is introduced, which aims at the efficient computation of polychromatic light fields. It was found that no significant increase of accuracy can be realized by usage of adapted spectral grids for spectral integration. It is presumed that this observation is caused by the changing shape of the light spectrum along the optical path.