An iterative scheme for numerical solution of steady incompressible viscous flows

An iterative solution scheme is proposed for application to steady incompressible viscous flows in simple and complex geometries. The iterative scheme solves the vorticity-stream function form of the Navier-Stokes equations in generalized curvilinear coordinates. The flow system of equations are cast into a Newton's iterative form which are solved using the modified strongly implicit procedure. The solution scheme is benchmarked using two test cases, namely: a shear-driven steady laminar flow in a square cavity; and a simple laminar flow in a complex expanding channel. The iterative process to steady-state convergence in both test cases is highly stable and the convergence rate is without spurious oscillations. At convergence, the flow solutions are second-order accurate.