A large-eddy simulation method for low Mach number flows using preconditioning and multigrid

Large-eddy simulation (LES) has become one of the major tools to investigate the physics of turbulent compressible and incompressible flows. At low Mach numbers the performance of LES codes developed for the conservation equations of compressible fluids deteriorates due to the presence of two different time scales associated with acoustic and convective waves. In many subsonic turbulent flows low Mach number regions exist, which require large integration times until a fully developed flow is established. In such cases, the efficiency of algorithms for compressible flows can be improved considerably by low Mach number preconditioning methods. In this paper an efficient method of solution for low subsonic flows is developed based on an implicit dual time stepping scheme combined with low Mach number preconditioning and a multigrid acceleration technique. To validate the efficiency and the accuracy of the method, large-eddy simulations of turbulent channel flow at Reτ = 590 and cylinder flow at Re = 3900 are performed for several Mach numbers and the data are compared with numerical and experimental findings from the literature. The speedup compared to a purely explicit approach is in the range of 6–40.