Combustion process is at the root of most energy production systems. This is especially the case for propulsion systems (piston engines/aeronautical turbines or rockets). The giant leaps performed in computer science over the past two decades have allowed us to use simulation to understand combustion in real configurations instead of only in academic laboratory burners. This presentation discusses the application of high performance computing for Computational Fluid Dynamics (CFD) in industrial cases for aeronautical turbines using the Large Eddy Simulation (LES) approach. Special attention is given to work performed under the INCITE program using the ALCF BlueGene/P to study to unsteady dangerous behaviours of flames, which these combustors often exhibit.