Simplified PN Approximations to the Equations of Radiative Heat Transfer and Applications

Simplified PN (SPN) approximations to the equations of radiative heat transfer are derived for optically thick, diffusive systems, and appropriate boundary conditions are formulated. The SPN equations are derived by an asymptotic analysis, while the boundary conditions are obtained from a variational analysis. Numerical comparisons of the SPN, equilibrium diffusion, and full transport equations are presented to demonstrate the accuracy and efficiency of the SPN approximations.