瞬态Navier-Stokes方程的一种新的全离散粘性稳定化方法

覃燕梅; 冯民富; 周天孝

doi:10.3879/j.issn.1000-0887.2009.07.004

瞬态Navier-Stokes方程的一种新的全离散粘性稳定化方法

doi: 10.3879/j.issn.1000-0887.2009.07.004

1.
内江师范学院数学与信息科学学院,四川内江 641112;2.四川省高等学校数值仿真重点实验室,四川内江 641112;3.电子科技大学应用数学学院, 成都 610054;4.四川大学数学学院, 成都 610064;5.航空计算技术研究所, 西安 710078

基金项目: 四川省科技攻关课题资助项目(05GG006-006-2);电子科技大学人才引进基金的资助

详细信息

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

中图分类号: O242.21
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出版历程
- 收稿日期: 2009-01-05
- 修回日期: 2009-05-18
- 刊出日期: 2009-07-15

A New Full Discrete Stabilized Viscosity Method for the Transient Navier-Stokes Equations

1.
Colledge of Mathematics and Information Sciences, Neijiang Normal University, Neijiang, Sichuan 641112, P. R. China;

摘要

摘要: 基于压力投影和梯形外推公式,对速度/压力空间采用等阶多项式逼近,针对高Reynolds数下的瞬态Navier-Stokes方程提出了一种新的全离散粘性稳定化方法．该方法不仅绕开了inf-sup条件的限制,克服了高Reynolds数下对流占优造成的不稳定性,而且在每一时间步上,只需要进行线性计算,从而减少了计算量．给出了稳定性证明,并得出了与粘性系数一致的误差估计．理论和数值结果表明该方法具有二阶精度．
- Reynolds数 /
- 压力投影 /
- 梯形外推公式 /
- 瞬态Navier-Stokes方程
Abstract: A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number(small viscosity coefficient)was proposed based on pressure projection and extrapolated trapezoidal rule.The transient Navier-Stokes equations are fully-discretized by continuous equal-order finite elements in space and reduced Crank-Nicolson scheme in time.The new stabilized method is stable and has a number of attractive properties.Firstly,the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pressure projection term.Secondly,the artifical viscosity parameter was added to the viscosity coefficient as a stability factor,so the system is antidiffusion.Finally,the method requires only the solution of one linear system per time step.Stability and convergence of the method was proved.The error estimation results show that the method has second order accuracy,and the constant in the estimation is independent of the viscosity coefficient.The numerical results were given,which demonstrate the advantage of the method presented.
- Reynolds number /
- pressure projection /
- extrapolated trapezoidal rule /
- the transient Navier-Stokes equations

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参考文献(14)

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[2]	Girault V,Raviart P.Finite Element Methods for the Navier-Stokes Equations[M].Berlin: Springer,1986.
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瞬态Navier-Stokes方程的一种新的全离散粘性稳定化方法

doi: 10.3879/j.issn.1000-0887.2009.07.004

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

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A New Full Discrete Stabilized Viscosity Method for the Transient Navier-Stokes Equations

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瞬态Navier-Stokes方程的一种新的全离散粘性稳定化方法

doi: 10.3879/j.issn.1000-0887.2009.07.004

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

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出版历程

A New Full Discrete Stabilized Viscosity Method for the Transient Navier-Stokes Equations

计量

出版历程

目录

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