Being able to ignite or reignite a gas turbine engine in a cold and rarefied atmosphere is a critical issue for many aeronautical gas turbine manufacturers. From a fundamental point of view, the ignition of the first burner and the flame propagation from one burner to another are two phenomena that are usually not studied. The present work presents ongoing and past Large Eddy Simulations (LES) on this specific subject and as investigated at CERFACS (European Centre for Research and Advanced Training in Scientific Computation) located in Toulouse, France. Validation steps and potential difficulties are underlined to ensure reliability of LES for such problems. Preliminary LES results on simple burners are then presented, followed by simulations of a complete ignition sequence in an annular helicopter chamber. For all cases and when possible, two-phase or purely gaseous LES have been applied to the experimentally simplified or the full geometries. For the latter, massively parallel computing (700 processors on a Cray XT3 machine) was essential to perform the computation. Results show that liquid fuel injection has a strong influence on the ignition times and the rate at which the flame progresses from burner to burner. The propagation speed characteristic of these phenomena is much higher than the turbulent flame speed. Based on an in-depth analysis of the computational data, the difference in speed is mainly identified as being due to thermal expansion and the flame speed is strongly modified by the main burner aerodynamics issued by the swirled injection.