A 2nd order numerical method for laminar flow at moderate to high Reynolds numbers - Entrance flow in a duct

This paper develops some improved 'upwind difference' approximations for the solution of the elliptic boundary value problems that arise in fluid flow and which are of special use when convective effects are dominant over diffusion. Barrett considered a one-dimensional analog of the vorticity stream function formulation of the Navier-Stokes equations, and developed a locally-exact technique of solution. It is shown how the locally exact technique may be generalized to multidimensional problems and used to solve the full Navier-Stokes equations. The process is shown to yield accurate predictions for developing channel flow.