Time-marching solution of incompressible Navier-Stokes equations for internal flow

Abstract A factored ADI finite-difference scheme has been developed for solution of the two dimensional incompressible Navier-Stokes equations by the artificial compressibility method. The scheme employs primitive variables with central differencing on a staggered grid. The resulting close coupling between pressure and velocity produces enhanced stability and eliminates the need for artificial damping. A spatially variable time step based on a fixed Courant number is used to improve computational efficiency. Numerical results have been obtained for flows in a straight channel, a curved rotating channel, and a driven cavity. In the latter case at Reynolds number of 10,000 with local cell Reynolds numbers as high as 100, a solution on a 40 × 40 stretched grid shows no spatial oscillations in the flow variables.