A fourth-order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

✍ Scribed by Zhenfu Tian; Yongbin Ge

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 256 KB
• Volume: 41
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.444

✦ Synopsis

Abstract

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.