HETEROGENEOUS MULTISCALE METHODS FOR ROUGH-WALL LAMINAR VISCOUS FLOW

We develop numerical multiscale methods for viscous fluid flow over a rough boundary. The goal is to derive effective boundary conditions, or wall laws, through high resolution simulations localized to the boundary coupled to a coarser simulation in the domain interior following the framework of the heterogeneous multiscale method. Rigorous convergence of the coupled system is shown in a simplified setting. Numerical experiments illustrate the utility of the method for more general roughness patterns and far field flow conditions.