In this study, numerical simulations of a low emission lab-scale non-premixed combustor are conducted and analyzed. The objectives are to provide new insight into the physical phenomena in the SPRF (Stagnation Point Reverse Flow) combustor built in the Georgia Tech Combustion Lab, and to compare three Large Eddy Simulation (LES) combustion models (Eddy Break-Up [EBU], Steady Flamelet [SF] and Linear Eddy Model [LEM]) for non-premixed combustion. The nominal operating condition of the SPRF combustor achieves very low NOx and CO emissions by combining turbulent mixing of exhaust gases with preheated reactants and chemical kinetics. The SPRF numerical simulation focuses on capturing the complex interaction between turbulent mixing and heat release. LES simulations have been carried out for a non-reactive case in order to analyze the turbulent mixing inside the combustor. The LES results have been compared to PIV experimental data and the code has been validated. The dominating features of the operational mode of the SPRF combustor (dilution of hot products into reactants, pre-heating and pre-mixing) have been analyzed, and results from the EBU-LES, SF-LES and LEM-LES simulations have been compared. Analysis shows that the LEM-LES simulation achieves the best agreement with the observed flame structure and is the only model that captures the stabilization processes observed in the experiments. EBU-LES and SF-LES do not predict the correct flow pattern because of the inaccurate modeling of sub-grid scale mixing and turbulence-combustion interaction. Limitations of these two models for this type of combustor are discussed.