Large Eddy Simulation (LES) of gas turbine combustors has gained traction as a key tool in the design process. Accurate prediction of the multiphysics of reacting flows — evaporating fuel spray, turbulent mixing, turbulent chemistry interaction, radiation, and conjugate heat transfer to name a few — is key to the accurate prediction of combustor performance. The overall solution time for a standard LES simulation on an industrial system can be burdensome because of the small time and length scales required to capture the aforementioned multiphysics to an acceptable level. Any performance improvements are therefore welcomed. In this paper, we compare the implicit non-iterative PISO solution procedure with the implicit iterative SIMPLE method for the Large Eddy Simulation of a Honeywell combustor using the commercial software, Simcenter STAR-CCM+ v13.04. Time averaged simulation results are validated against rig data. Results show that the PISO solution method provides results which are similar to those found using the SIMPLE method, and accurate when compared to rig data, but at up to a 3.4X speed-up for this liquid fueled gas turbine combustor.