求解Stokes方程的最小二乘等几何分析方法

陈德祥 1; 徐自力 1; 刘石 2; 冯永新 2

doi:10.7652/xjtuxb201305009

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求解Stokes方程的最小二乘等几何分析方法

更新时间：2025-07-09

- 求解Stokes方程的最小二乘等几何分析方法
- Least Squares Isogeometric Analysis for Stokes Equation
- 西安交通大学学报 2013年47卷第5期页码：51-55
- 作者机构：
  
  西安交通大学机械结构强度与振动国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
  
  : 2012-09-17。作者简介: 陈德祥(1979—),男,博士生;徐自力(通信作者),男,教授,博士生导师。基金项目: 国家“973计划”资助项目(2011CB706505);国家自然科学基金资助项目(50675169)
- DOI：10.7652/xjtuxb201305009
  中图分类号： O241.82
- 网络首发：2013-05-10，
  
  纸质出版：2013
- 稿件说明：
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陈德祥 1, 徐自力 1, 刘石 2, 等. 求解Stokes方程的最小二乘等几何分析方法[J]. 西安交通大学学报, 2013,47(5):51-55.

Least Squares Isogeometric Analysis for Stokes Equation[J]. 2013, 47(5): 51-55.
陈德祥 1, 徐自力 1, 刘石 2, 等. 求解Stokes方程的最小二乘等几何分析方法[J]. 西安交通大学学报, 2013,47(5):51-55. DOI： 10.7652/xjtuxb201305009.

Least Squares Isogeometric Analysis for Stokes Equation[J]. 2013, 47(5): 51-55. DOI： 10.7652/xjtuxb201305009.

摘要

针对采用C

型基函数的最小二乘有限元需增加辅助独立变量的问题

提出了一种改进的方法——最小二乘等几何分析方法。采用具有高阶光滑性的非均匀有理B样条作为基函数

直接用原始变量定义最小二乘泛函

建立了求解Stokes方程的改进算法。该方法不需引入新独立变量

且网格可在数值分析中自动生成并能精确表达区域的几何形状。用所提出的方法求解了二维不可压Stokes流动

计算结果与解析解符合较好

表明该方法可用于Stokes方程的求解

提高基函数光滑性的k细化具有指数收敛速度。

Abstract

Additional independent variables are needed in the least squares finite element method(LSFEM)using C

element. An improved method

the least squares isogeometric analysis(LSIGA)was proposed to substitute LSFEM. In LSIGA

the high continuity non-uniform rational B-spline(NURBS)was applied as the basis function and only the primitive variables in the Stokes equation were adopted to define the least squares functional. LSIGA does not need additional independent variables

and it can generate the mesh automatically in analysis and the mesh represents the domain geometry exactly. An incompressible 2D Stokes flow was solved with the present method. The numerical solution agrees well with the analytical solution. The results show that the method proposed is applicable for solving the Stokes equation and its k-refinement increasing the NURBS continuity in analysis has an exponential con

vergence rate.

关键词

Keywords

references

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BUFFA A, FALCO C De, SANGALLI G. Isogeometric analysis: stable elements for the 2D Stokes equation [J]. International Journal for Numerical Methods in Fluids, 2011, 65(11/12): 1407-1422.

祝雪峰, 马正东, 胡平. 几何精确非协调等几何NURBS有限元 [J]. 固体力学学报, 2012, 33(5): 487-492.

ZHU Xuefeng, MA Zhengdong, HU Ping. Nonconforming isogeometric analysis based on NURBS with exact geometry [J]. Chinese Journal of Solid Mechanics, 2012, 33(5): 487-492.

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