求解二维不可压缩Navier-Stokes方程的混合型微分求积法

孙建安; 朱正佑

求解二维不可压缩Navier-Stokes方程的混合型微分求积法

孙建安¹,
朱正佑²

1.
西北师范大学物理系, 兰州730070;
2.
上海大学数学系, 上海市应用数学和力学研究所, 上海200072

详细信息

作者简介:
孙建安(1964~ ),男,副教授,主要从事流体力学数值方法的研究.

中图分类号: O357.1
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出版历程
- 收稿日期: 1998-01-06
- 修回日期: 1999-04-21
- 刊出日期: 1999-12-15

A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations

Sun Jian'an¹,
Zhu Zhengyou²

1.
Department of Physics, Northwest Normal University, Lanzhou 730070, P R China;
2.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;

摘要

摘要: 微分求积法(DQM)能以较少的网格点求得微分方程的高精度数值解,但采用单纯的微分求积法求解二维不可压缩Navier-Stokes方程时,只能对低雷诺数流动获得较好的数值解,当雷诺数较高时会导致数值解不收敛。为此,提出了一种微分求积法与迎风差分法混合求解二维不可压缩Navier-Stokes方程的预估-校正数值格式,用伪时间相关算法以较少的网格点获得了较高雷诺数流动的数值解。作为算例,对1:1和1:2驱动方腔内的流动进行了计算,得到了较好的数值结果。
- 数值方法 /
- 微分求积法 /
- Navier-Stokes方程
Abstract: Differential quadrature method(DQM)is able to obtain highly accurate numerical solutions of differential equations just using a few grid points.But using purely differential quadrature method, good numerical solutions of two-dimensional incompressible Navier-Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow.For this reason,in this paper a combinative predicting-correcting numerical scheme for solving two-dimensional incompressible Navier-Stokes equations is presented by mixing upwind difference method into differential quadrature one.Using this scheme and pseudo-time-dependent algorithm,numerical solutions of high Reynolds number flow are obtained with only a few grid points.For example,1:1 and 1:2 driven cavity flows are calculated and good numerical solutions are obtained.
- numerical method /
- differential quadrature method /
- Navier-Stokes equations

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参考文献(10)

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