Approximate wall boundary conditions in the large-eddy simulation of high reynolds number flow

The near-wall regions of high Reynolds numbers turbulent flows must be mode lled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separa ted flows on coarse grids in which the near-wall regions are not resolved a nd are instead represented by approximate wall boundary conditions. The sim ulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acce ptable results found in many cases in the core of the flow far from the wal ls, provided there is adequate numerical resolution, but with poorer result s generally found near the wall. Deficiencies in this approach are caused i n part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing large -eddy simulation on coarse grids. A promising new method for developing wal l models from optimal control theory is also discussed.