Estimation of the stability margins of combustion processes in the combustion chamber of a gas turbine engine is a vital task of current subsonic and supersonic propulsion engineering and this article describes the approach to its Computational Fluid Dynamics simulation. The aim of the work is to create and verify a methodology for assessing the stability regimes of combustion processes in the combustion chamber of a gas turbine engine based on an artificial simulation of the excitation of non-stationary processes in the temperature-pressure parameters using “ANSYS Fluent”. The further comparison of the computed results and the real data of the physical experiment in the model device will take place to verify the method. During the research this methodology and a software product will be developed for computing the characteristics of the combustion processes before and after the excitation of the artificial unstable process. This technique, when verified, will allow to clarify the instability limits for specific operating modes (engine stall, flame suppression, lean flameout) of existing and projected gas turbine engines. The obtained numerical results allow us to make an assumption about the fundamental possibility of obtaining convergent solutions in close according with the future experimental data.