AlAA 96-2089 Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach

A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finitevolume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5'h) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a linerelaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the linerelaxation procedure in the soiucion of the Foisson equation for pressure. Tiis procedure is applied to a Couette flow problem u s ing a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5'h-order u p wind differencing and a modified production term in the Baldwin-Barth oneequation turbulence model are used with adequate grid resolution. * Research Scientist, Senior Member AIAA ** Branch Cheif, Associate Fellow AIAA Copyright 01996 American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royaltyfree license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner.