A Hybrid Discrete Ordinates Spherical Harmonics Method For Solution Of The Radiative Transfer Equation In Multi Dimensional Participating Media

Abstract: The Radiative Transfer Equation (RTE) is a multi-dimensional integro - differential equation. It is difficult to obtain an exact analytical solution to the RTE even for simple one - dimensional cases due of its directional nature. As a result, approximate numerical methods must be used to solve the RTE. The two most popular methods that are currently used to solve the RTE are the Method of Spherical Harmonics, PN approximation, and the Discrete Ordinates Method, DOM or SN approximation. However, neither of these methods exhibit good accuracy over the entire range of optical thickness of practical interest. The PN approximation, although it shows good accuracy for optically thick regimes, it is not accurate for optically thin media and in scenarios in which radiation propagation is strongly directional, such as that of a medium bounded by a combination of hot and cold walls. The SN method, on the other hand, does show promising accuracy over a wide range of optical thickness. However, it suffers from ray effects in optically thin media, resulting in locally unphysical solutions. In optically thick media, the strongly coupled directional equations in DOM, renders the method computationally very expensive for obtaining accurate results. Keeping in mind the advantages of each of the afore-mentioned methods and the regimes in which they are accurate, a new robust and computationally efficient hybrid method that has acceptable accuracy over a wide range of optical thickness is proposed, developed, and demonstrated in this thesis.