AN UPWIND DIFFERENCING SCHEME FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

The steady-state incompressible Navier-Stokes equations in two dimensions are solved numerically using the artificial compressibility formulation. The convective terms are upwind differenced using a flux-difference split approach that has uniformly high accuracy throughout the interior grid points. The viscous fluxes are differenced using second-order accurate central differences. The numerical system of equations is solved using an implicit line relaxation scheme. The scheme is applicable to both steady-state and unsteady flow computations. In the current work steady-state applications are emphasized. Characteristic boundary conditions are formulated and used in the solution procedure. The overall scheme is capable of being run at extremely large pseudo-time steps, leading to fast convergence. Three test cases are presented to demonstrate the accuracy and robustness of the code. These are the flow in a square driven cavity, flow over a backward facing step, and flow around a two-dimensional circular cylinder.