This paper presents the in-situ combustion concept and preliminary numerical results in a one stage turbine combustor. The main purpose of the simulation is to assess the stability of the in situ combustion with respect to the unsteadiness induced by the rotor-stator interaction. In order to identify information on the sources of instability for this complex flow, proper orthogonal decomposition technique is adopted to analyze the natural patterns and couplings between various modes of pressure, temperature, velocity and chemical production rate distributions. The major find of this investigation is that contrary to all other primitive variables, the reconstruction of chemical reaction rates needs a larger number of energy modes to attain a reasonable normalized error.