Abstract The paper presents a numerical study of the mechanisms driving thermoacoustic instabilities in a lean partially premixed combustor in conditions representative of gas turbine combustion systems. Various combustion models and modeling approaches able to predict the onset of thermoacoustic instabilities are examined and applied to the experimental test rig in order to assess their validity. The influence of the imposed acoustic and thermal boundary conditions on characterization of the coupling between heat release rate fluctuations and the acoustic field is investigated. Predicted data is used to improve the understanding of mutual interactions between pressure fluctuations and unsteady heat release in the unstable combustors which play an essential role in characterizing limit-cycle behavior. The mean convective time delay between heat release and the perturbation in the flow is used to determine the stability condition of the combustor. The study shows that heat transfer is important parameter regulating pressure oscillations.