An efficient semi-implicit compressible solver for large-eddy simulations

In this paper, a pressure-based semi-implicit algorithm for compressible flows is described. This type of solver is of great interest in combustion devices where the flow speed is small but where the unsteady heat release can be coupled to the acoustic modes and lead to instabilities. The fractional-step method used in this algorithm is based on a characteristic splitting, which clearly separates the acoustics from the advection. This splitting allows to use adapted numerics for these different time-scales. The algorithm is second-order in space and time for linear acoustics and for low-Mach advection without iterating the time-step. Moreover, when kinetic-energy conserving schemes are used for the predictor step, the algorithm discretely conserves the kinetic energy in the low-Mach limit. All these properties are illustrated on simple test cases and the algorithm is finally validated by performing the LES of the cold flow of an industrial burner.