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论文摘要

三维对流扩散方程在高雷诺数的自动迎风与斜迎风数值解

Auto Up-wind and Skew Up-wind Numerical Solution of 3D Convection diffusion Equation under High Reynolds Number

作者:李力(西安理工大学 西北水资源与环境生态教育部重点实验室,陕西 西安 710048);冯民权(西安理工大学 西北水资源与环境生态教育部重点实验室,陕西 西安 710048);郑邦民(武汉大学 水电学院,湖北 武汉 430072)

Author:(Key Lab. Resources and Environment Ecology of MOE at XAUT,Xi’an 710048,China);(Key Lab. Resources and Environment Ecology of MOE at XAUT,Xi’an 710048,China);(School of Hydraulic and Electric Power,Wuhan Univ., Wuhan 430072,China)

收稿日期:2007-11-02          年卷(期)页码:2008,40(4):41-46

期刊名称:工程科学与技术

Journal Name:Advanced Engineering Sciences

关键字:对流扩散;自动迎风;斜迎风;高雷诺数

Key words:convection and diffusion;auto up-wind;skew up-wind;high Reynolds number

基金项目:国家自然科学基金资助项目(50679071)

中文摘要

为了使三维对流扩散方程在高Reynolds数情况下保持自动迎风与斜迎风性质,在二维格式的基础上,重点分析了三维情况下具有非线性性质的对流项离散格式的构造。通过指数函数构造迎风权系数,不会形成某一个网格点的贡献绝对占优的不合理情况。在各方向流速不等时,得出主流速及其权系数。通过空间几何变换,从平面中心点拓展到边棱中点和角点,得出标准27点格式的权系数。格式包括了角点的贡献,从而保持了斜迎风性质。通过与有限分析法比较,结果表明,数值格式随Reynolds数的增大,不会蜕化为简单迎风。本方法可广泛应用于流场、温

英文摘要

In order to make the 3D CD equation to maintain auto up-wind and skew up-wind under high Reynolds number, on the basis of 2D scheme, this paper focuses on development of difference scheme of 3D non-liner convection item. Exponent function is used as the weighted coefficient of auto up-wind, and the irrational case some grid point gained absolute advantage is not formed. When the velocities of every direction are not equal, the primary flow velocity and weighted coefficients are received. Weighted coefficients of 27 points’ scheme are obtained from center points of face to middle ones of edge to corner ones via geometrical transformation of space. It takes into account the effect of corner points, so it kept auto up wind. It is compared with FA method and results show the scheme can’t change to simple up-wind by the increasing of Reynolds number. It can be applied to the solution of fluid-flow, temperature and concentration problems.

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