Navier-Stokes方程几种稳定化有限元算法数值比较

数学物理学报 ›› 2016, Vol. 36 ›› Issue (3): 543-557.

Navier-Stokes方程几种稳定化有限元算法数值比较

文娟¹, 何银年², 黄鹏展³, 李敏⁴

1 西安理工大学理学院西安 710048;
2 西安交通大学数学与统计学院西安 710049;
3 新疆大学数学与系统科学学院乌鲁木齐 830046;
4 云南开放大学光电工程学院昆明 650223

收稿日期:2015-09-02 修回日期:2016-02-03 出版日期:2016-06-26 发布日期:2016-06-26
作者简介:文娟,zhongnanjicuan@163.com
基金资助:
国家自然科学基金（11271298，11571275）和西安理工大学博士启动金项目（109-256211419）资助

Numerical Investigations on Several Stabilized Finite Element Methods for the Navier-Stokes Problem

Wen Juan¹, He Yinnian², Huang Pengzhan³, Li Min⁴

1 School of Sciences, Xi'an University of Technology, Xi'an 710048;
2 Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049;
3 College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046;
4 College of optoelectronic engineering, Yunnan Open University, Kunming 650223

Received:2015-09-02 Revised:2016-02-03 Online:2016-06-26 Published:2016-06-26
Supported by:
Supported by the NSFC (11271298, 11571275) and a research grant for doctorate from Xi'an University of Technology (109-256211419)

摘要/Abstract

摘要：

该文比较了基于低次等阶有限元对求解定常Navier-Stokes方程的几种稳定化有限元算法. 通过比较可以看出，在求解大雷诺数Navier-Stokes方程时，多尺度增量有限元算法从稳定性和计算精度方面来说是一种不错的方法.

关键词: 稳定化方法, P₁/P₁有限元对, Inf-Sup条件, 混合有限元, Navier-Stokes方程

Abstract:

In this paper, several stabilized finite element methods based on the lowest equal-order finite element pairs (P₁/P₁ or Q₁/Q₁) for the steady Navier-Stokes problem are investigated. The methods include penalty, regular, local Gauss integration and multiscale enrichment method. Comparisons among them show that the multiscale enrichment method we constructed is a favorite method in terms of stability and accuracy at higher Reynolds numbers for the Navier-Stokes problem.

Key words: Stabilized methods, P₁/P₁ elements, Inf-Sup condition, Mixed finite element methods, Navier-Stokes problem

中图分类号:

O241.182

文娟, 何银年, 黄鹏展, 李敏. Navier-Stokes方程几种稳定化有限元算法数值比较[J]. 数学物理学报, 2016, 36(3): 543-557.

Wen Juan, He Yinnian, Huang Pengzhan, Li Min. Numerical Investigations on Several Stabilized Finite Element Methods for the Navier-Stokes Problem[J]. Acta mathematica scientia,Series A, 2016, 36(3): 543-557.

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