Wall Models for Large-Eddy Simulation Based on Optimal Control Theory

摘要

Large-eddy simulation (LES) requires very high resolution in high Reynolds number, attached turbulent boundary layers due to the need to capture the small, dynamically important near-wall eddies. Wall modeling enables LES to be performed on grids that do not resolve these eddies by providing approximate boundary conditions to the simulation. Unfortunately, wall models based on purely physical reasoning often lead to an inaccurate LES, particularly on coarse grids and at high Reynolds numbers, because they do not account for numerical and subgrid scale modeling errors. To compensate for these errors, a wall model based on optimal control theory has been developed that differs from previous approaches in two significant ways. First, the computational expense of the optimization procedure has been reduced by an order of magnitude (with respect to previous control-based wall models) by defining the optimization problem only near the boundaries and carefully constructing the equations governing the optimization problem. Second, no a priori information is required since a near-wall RANS solver is coupled with the LES to provide the controller with information about the mean velocity profile. This approach has been successfully tested in high Reynolds number plane channel flow.