A One-Dimensional-Subgrid Based Wall Function for Use With Coarse Near-Wall Meshes

A common alternative to full resolution of the near-wall region in computational fluid dynamics (CFD) simulations is the use of wall functions that decrease the mesh requirements in this region. This paper presents an alternative to current wall functions based on numerically approximating a turbulent velocity profile using a one-dimensional subgrid contained within wall-adjacent control volumes (cells). Use of the subgrid allows approximation of boundary layers of varying height relative to the first layer sizing. Most significantly, this includes boundary layers with heights smaller than the first layer cells themselves. Use of the subgrid allows wall adjacent primary grid sizes to vary from low-Re model sizing of y⁺ ≈ 1 to grid sizes of y⁺ ∼ 1000 or more without significant loss in accuracy versus fully resolved simulations, and with computational costs similar to currently used wall functions. The development of the new method is presented and results are shown from two demonstration test cases — flow over a flat plate and axial flow over a cylindrical body. The results are compared to low-Re modeling with a very fine near wall mesh, and to currently used wall functions.