Standard numerical schemes for coupled parallel flow over porous layers

In this work, we develop finite difference schemes of various orders of accuracy that are suitable for the simulation of flow through and over porous layers. The flow through the porous layer is assumed to be governed by a Brinkman-type equation, and that through free-space by the Navier–Stokes equations. Matching conditions at the interface between layers are invoked to derive numerical expressions for the velocity and shear stress. Results are compared with the exact solution of flow through a channel bounded by a porous layer.