An overview is provided of the recent advances in performing LES in complex combustor geometries using a non-dissipative, massively parallel, unstructured grid solver (CDP). A new numerical algorithm that is discretely energy conserving on hybrid unstructured grids is developed. This allows simulations at high Reynolds numbers without the use of numerical dissipation. This LES methodology has been extended to include advanced turbulent combustion models and a Lagrangian particle tracking methodology for simulating turbulent multiphase flows. Results for single and multi-phase flow simulations in realistic Pratt & Whitney (P&W) combustor geometries are discussed.