The Trapped Vortex Combustor (TVC) is a challenging configuration where flame stabilization is achieved through the presence of a cavity. The present work describes an unsteady non-reacting and reacting annular TVC flow studied with Large-Eddy Simulation and Immersed Boundaries Method. The combustion model is based on tabulated chemistry associated with a presumed PDF. The effects of local strain rate and of heat losses are included in the modelling. The simulations are compared with experimental results and the performance of the modelling closures is discussed