An angular reduced order model for radiative transfer in non grey media

Abstract : This paper investigates a reduced order model for the angular discretisa-tion of the radiative transfer equation (RTE) when considering non grey participating gases. The key idea is to use a global model for the gas ra-diative properties and to derive an angular reduced order model, based on the Proper Orthogonal Decomposition (POD) method, for each absorption coefficient class independently. Angular POD basis functions are extracted from high order S N reference solutions. A finite element approach is used to discretised the RTE in space and angle and the POD angular matrices of the reduced system are easily constructed from the S N angular matrices of the reference solutions. The angular POD basis sets are truncated at different levels depending on the absorption coefficient class in order to optimally compute the total radiative power. The method is applied to solve the radia-* Corresponding author. tion field associated to an air/H 2 O mixture flowing in a square differentially heated cavity, with black isothermal walls and diffuse reflecting adiabatic walls. Results show that the POD model is very accurate and efficient for treating the thick classes but it suffers from a low convergence rate for the thin classes. For computing the radiative power, the reduced order model allows to reduce the averaged number of angular basis functions of an order of magnitude and to reduce the CPU time by a factor 2 to 3 to reach a given level of accuracy, compared to a standard S N method.