An efficient wall model for large-eddy simulation based on optimal control theory

Large-eddy simulation is currently very expensive for high Reynolds number attached flows due to the need to resolve the wall layer. In order to reduce this expense, wall modeling has been proposed to provide approximate boundary conditions to the LES that allow the wall layer to be unresolved. Unfortunately, subgrid scale modeling errors and numerical errors are important in this region when a coarse grid is used, necessitating a wall model that can compensate for their effects. Optimal control theory has been used to provide such models in the past, but is impractical for complex flows due to the need to provide a target mean velocity profile and the computational expense involved with solving gradient-based optimization problems. In this paper we address the latter issue by reformulation of the optimization problem to include only data near the wall. Further approximations have been made to the Navier-Stokes and adjoint equations used in the optimization process that significantly reduce the computational cost. Results will be presented comparing this method with other control-based and standard wall models.