Toward real-time high-fidelity simulation using integral boundary layer modeling

One of the greatest challenges to using large-eddy simulations (LES) in engineering applications is the large number of grid points required near walls. To mitigate this issue, researchers often couple LES with a simplified model of the flow close to the wall, known as the wall model. One feature common to most wall models is that the first few (about 3) grid points must be located below the inviscid log-layer, and the grid must have near-isotropic resolution near the wall. Hence, wall-modeled LES may still require a large number of grid points in both the wall-normal and span-wise directions. Because of these requirements, wall-modeled LES is still unfeasible in many applications. We present a new formulation of wall-modeled LES that is being developed to address this issue. In this formulation, LES is used to solve only for the features of the velocity field that can be adequately represented on the LES grid. The effects of the unresolved features are captured by imposing an integral balance of kinetic energy in the near-wall region. This integral energy balance translates into a dynamic partial differential equation defined on the walls, which is coupled to the LES equations. We discuss details of the new formulation and present results obtained in laminar channel flows.
Comment: 10 pages, 7 figures, final report of the 16th biennial summer program of the Center for Turbulence Research at Stanford University