A two-scale method for radiative heat transfer in non-grey absorbing and emitting media

Multiscale radiative heat transfer (RHT) problems are formulated and methods to approximate their numerical solutions are developed. We focus on RHT problems in participating media with heterogeneous optical properties leading to both optically thick and thin regimes within the same media spectrum. By introducing a diffusive scale and using an asymptotic expansion in the RHT equations we formulate the simplified PN approximations. The optical spectrum is decomposed in wavelength bands and the RHT equations are solved for bands with low absorption while the simplified PN equations are solved for bands with high absorption. The hybrid models solve the multiscale RHT more accurately than the simplified PN approximations and with a computational costs less than using the full RHT solver. Accuracy and effectiveness of the proposed models are demonstrated on three-dimensional RHT problems arising in combustion systems.