Model-based near-wall reconstructions for immersed-boundary methods

In immersed-boundary methods, the cost of resolving the thin boundary layers on a solid boundary at high Reynolds numbers is prohibitive. In the present work, we propose a new model-based, near-wall reconstruction to account for the lack of resolution and provide the correct wall shear stress and hydrodynamic forces. The models are analytical versions of a generalized version of the two-layer model developed by Balaras et al. (AIAA J 34:1111–1119, 1996) for large-eddy simulations. We will present the results for the flow around a cylinder and a sphere, where we use Cartesian and cylindrical coordinate grids. We will demonstrate that the proposed treatment reproduces very accurately the wall stress on grids, which are one order of magnitude coarser compared to well-resolved simulations.