Navier-Stokes方程的局部投影稳定化方法

覃燕梅; 冯民富; 罗鲲; 吴开腾

doi:10.3879/j.issn.1000-0887.2010.05.013

Navier-Stokes方程的局部投影稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.05.013

四川省高等学校数值仿真重点实验室,四川内江 641112;2.内江师范学院数学与信息科学学院,四川内江 641112;3.四川大学数学学院,成都 610064

基金项目: 国家自然科学基金资助项目(10872085);四川省科技攻关课题资助项目(05GG006-006-2);内江师范学校青年科研项目(09NJZ-6)的资助

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作者简介:
覃燕梅(1980- ),女,四川青神人,讲师,硕士(联系人.Tel:+86-832-5063638;E-mail:qinyanmei0809@163.com);冯民富(1964- ),男,四川人,教授,博士(E-mail:fmf@wtjs.cn).

中图分类号: O242.21
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出版历程
- 收稿日期: 2009-10-26
- 修回日期: 2010-03-22
- 刊出日期: 2010-05-15

Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations

Key Laboratory of Numberical Simulation of Sichuan Province, Neijiang, Sichuan 641112, P. R. China;

摘要

摘要: 将Matthies，Skrzypacz和Tubiska的思想从线性的Oseen方程拓展到了非线性的Navier-Stokes方程，针对不可压缩的定常Navier-Stokes方程，提出了一种局部投影稳定化有限元方法．该方法既克服了对流占优，又绕开了inf-sup条件的限制．给出的局部投影空间既可以定义在两种不同网格上，又可以定义在相同网格上．与其他两级方法相比，定义在同一网格空间上的局部投影稳定化格式更紧凑．在同一网格上，除了给出需要bubble函数来增强的逼近空间外，还特别考虑了两种不需要用bubble函数来增强的新的空间．基于一种特殊的插值技巧，给出了稳定性分析和误差估计．最后，还列举了两个数值算例，进一步验证了理论结果的正确性．
- 局部投影 /
- Navier-Stokes方程 /
- Reynolds数
Abstract: The results of Matthies, Skrzypacz and Tubiska for the Oseen problem to the Navier-Stokes problem were extended. For the stationary incompressible Navier-Stokes equations, a local projection stabilized finite element scheme was proposed. The schem eovercomes convection dominated and ameliorates the restrictiveinf-supcondition. Local projection schemes were derived not only as a two-level approach but also for pairs of spaces which were defined on the samemesh. This class of stabilized schemes uses approxmiation and projection spaces defined on the same mesh and leads to much more compact stencils than in the two-level approach. On the same mesh, bes ides the class of local projection stabilization by enrichment of the approximation spaces, two new classes of local projection stabilization of the approximation spaces which dont. need to be enriched by bubble functions are derived. Based on a special in terpolation, the stability and an optimal priorierror estimates were shown. Finally, the numerical tests and the numerical computations show that the numerical results agree with some ben chmark solutions, which further poved the correctness of the theoretical analysis.
- local projection /
- the Navier-Stokes equations /
- Reynolds number

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参考文献(22)

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Navier-Stokes方程的局部投影稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.05.013

作者简介:
覃燕梅(1980- ),女,四川青神人,讲师,硕士(联系人.Tel:+86-832-5063638;E-mail:qinyanmei0809@163.com);冯民富(1964- ),男,四川人,教授,博士(E-mail:fmf@wtjs.cn).

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Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations

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留言板

Navier-Stokes方程的局部投影稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.05.013

作者简介: 覃燕梅(1980- ),女,四川青神人,讲师,硕士(联系人.Tel:+86-832-5063638;E-mail:qinyanmei0809@163.com);冯民富(1964- ),男,四川人,教授,博士(E-mail:fmf@wtjs.cn).

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出版历程

Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations

计量

出版历程

目录

作者简介:
覃燕梅(1980- ),女,四川青神人,讲师,硕士(联系人.Tel:+86-832-5063638;E-mail:qinyanmei0809@163.com);冯民富(1964- ),男,四川人,教授,博士(E-mail:fmf@wtjs.cn).