Efficient ADI and spline ADI methods for the steady-state Navier-Stokes equations

Napolitano (1980) has developed an alternating direction implicit (ADI) technique for the calculation of viscous, incompressible, steady flows past an arbitrary, two-dimensional body. The considered approach makes use of the vorticity-stream function Navier-Stokes equations in a system of general body-fitted coordinates. The major limitation of the proposed ADI approach is related to its use of central differences. This utilization of central differences limits the applicability of the ADI method to low Reynolds number flows, or to separation-free high Reynolds number flows. The present investigation is concerned with a procedure for improving the ADI technique developed by Napolitano. This procedure is based on the employment of incremental variables. The improved technique is more stable and capable of resolving high Reynolds number separated flows, while maintaining the second-order accuracy of the numerical-viscosity-free central differences.