A methodology for the computation of azimuthal combustion instabilities which can occur in annular combustors is proposed in this work. A thermoacoustic numerical tool using the n - tau model for the coupling of acoustic and combustion is required to solve the Helmholtz equation in reactive media. The methodology is based on the Independence Sector Assumption in Annular Combustor (ISAAC) which states that the heat release fluctuations in a given sector are driven only by the fluctuating mass flow rates due to the velocity perturbations through its own swirler. This assumption is first discussed with respect to a Large Eddy Simulation of an annular combustor. The methodology is then applied to an academic annular test case which exhibits amplified or damped, standing or rotating azimuthal eigenmodes depending on parameters n and tau.