A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations
A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations
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DOI：
10.1002/fld.444
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发表时间：
2003-02
影响因子：
1.8
通讯作者：
Z. Tian;Y. Ge
中科院分区：
文献类型：
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作者：
Z. Tian;Y. Ge
制定了九点二维模板上的四阶紧凑有限差分格式，用于使用流函数-涡度公式求解二维不可压缩流体流动和传热的稳态纳维-斯托克斯/布辛斯克方程。新的四阶紧凑方案的主要特征是它允许对所有物理感兴趣的瑞利数 Ra 和尝试的所有普朗特数 Pr 进行点连续过松弛 (SOR) 或点连续欠松弛迭代。利用基准解获得了方形腔内自然对流模型问题的数值解，并与文献中的一些准确结果进行了比较。版权所有 © 2003 约翰·威利父子有限公司
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.