Surface-sampled simulations of turbulent flow at high Reynolds number

Funding information European Commission Horizon 2020, Grant/Award Number: 671571; Engineering and Physical Sciences Research Council (EPSRC), Grant/Award Number: EP/L000261/1 Summary A new approach to turbulence simulation, based on a combination of large eddy simulation (LES) for the whole flow and an array of non–space-filling quasi-direct numerical simulations (QDNS), which sample the response of near-wall turbulence to large-scale forcing, is proposed and evaluated. The technique overcomes some of the cost limitations of turbulence simulation, since the main flow is treated with a coarse-grid LES, with the equivalent of wall functions supplied by the near-wall sampled QDNS. Two cases are tested, at friction Reynolds number Reτ = 4200 and 20000. The total grid point count for the first case is less than half a million and less than 2 million for the second case, with the calculations only requiring a desktop computer. A good agreement with published direct numerical simulation (DNS) is found at Reτ = 4200, both in the mean velocity profile and the streamwise velocity fluctuation statistics, which correctly show a substantial increase in near-wall turbulence levels due to a modulation of near-wall streaks by large-scale structures. The trend continues at Reτ = 20000, in agreement with experiment, which represents one of the major achievements of the new approach. A number of detailed aspects of the model, including numerical resolution, LES-QDNS coupling strategy and subgrid model are explored. A low level of grid sensitivity is demonstrated for both the QDNS and LES aspects. Since the method does not assume a law of the wall, it can in principle be applied to flows that are out of equilibrium.