This paper describes the approach to the computational fluid dynamics simulation of an aeronautic combustor. First of all, the combustion chamber geometry is presented and described. Then, the numerical models chosen for the flow field simulation are discussed. The main peculiarities of this fluid dynamic simulation are connected to the complex geometry, which has to be accurately represented, and to the liquid fuel entering the combustor, which undergoes a process of breakup and atomization due to injection. The fuel liquid droplets are then made to evaporate by the heat transfer coming from the flame inside the combustor. A turbulence model is also activated, to account for the effect of local flow recirculation and vortices on local temperature variation. The main objective of this study is to identify possible critical high temperature spots in the flow field, which might heat the metal shell of the combustor excessively and therefore to optimize the position of the dilution holes located onto the combustor walls. A first validation of the simulation approach has been done comparing the outlet temperature of the gases as obtained by the CFD, and the temperature in the same position, obtained using a numerical code for prediction.