Lean premixed combustion technology became state of the art in recent heavy-duty gas turbines and aeroengines. In combustion chambers operating under fuel-lean conditions, unsteady heat release can augment pressure amplitudes, resulting in component engine damages. In order to achieve deeper knowledge concerning combustion instabilities, it is necessary to analyze in detail combustion processes. The current study supports this by conducting a numerical investigation of combustion in a premixed swirl-stabilized methane burner with operating conditions taken from experimental data that were recently published. It is a follow-up of a previous paper from Farisco et al., 2019 where a different combustion configuration was studied. The commercial code ANSYS Fluent has been used with the aim to perform steady and transient calculations via Large Eddy Simulation (LES) of the current confined methane combustor. A validation of the numerical data has been performed against the available experiments. In this study, the numerical temperature profiles have been compared with the measurements. The heat release parameter has been experimentally and numerically estimated in order to point out the position of the main reaction zone. Several turbulence and combustion models have been investigated with the aim to come into accord with the experiments. The outcome showed that the combustion model Flamelet Generated Manifold (FGM) with the k-ω turbulence model was able to correctly simulate flame lift-off.