Simulation of fluid flow in 'rough' contact interfaces using hierarchical, heterogeneous and anisotropic approximation

Thin fluid flow in contact interfaces between solids with rough surfaces is often described by the Reynolds equation, known to overestimate the fluid velocity in fractures compared to full Navier-Stokes equations (NSE). The resolution of NSE is difficult if a fine surface discretisation is needed and/or if contact is taken into account. We propose a novel approach considering the flow governed by NSE in a single layer of prism elements. Using the hierarchical basis approximation, we can interpolate the velocity profile across the thickness by polynomials of an arbitrary order.