An artificial boundary condition for two-dimensional incompressible viscous flows using the method of lines

We design an artificial boundary condition for the steady incompressible Navier-Stokes equations in streamfunction-vorticity formulation in a flat channel with slip boundary conditions on the wall. The new boundary condition is derived from the Oseen equations and the method of lines. A numerical experiment for the non-linear Navier-Stokes equations is presented The artificial boundary condition is compared with Dirichlet and Neumann boundary conditions for the flow past a rectangular cylinder in a flat channel. The numerical results show that our boundary condition is more accurate.