A discrete artificial boundary condition for steady incompressible viscous flows in a no-slip channel using a fast iterative method

We design a discrete artificial boundary condition for the steady incompressible Navier-Stokes equations in stream function vorticity formulation in an infinite channel. The new boundary condition is derived from a linearized Navier-Stokes system and a fast iterative method. Numerical experiments for the nonlinear Navier-Stokes equations are presented. The discrete artificial boundary condition is compared to Dirichlet and Neumann boundary conditions for the flow over a forward or backward facing step and for flow past a rectangular cylinder. Numerical results show that our boundary condition is very effective.