## 留言板

 引用本文: 汤波, 李俊峰, 王天舒. 带自由液面粘性流体运动的最小二乘有限元模拟[J]. 应用数学和力学, 2008, 29(7): 855-863.
TANG Bo, LI Jun-feng, WANG Tian-shu. Viscous Flow With Free Surface Motion by Least Square Finite Element Method[J]. Applied Mathematics and Mechanics, 2008, 29(7): 855-863.
 Citation: TANG Bo, LI Jun-feng, WANG Tian-shu. Viscous Flow With Free Surface Motion by Least Square Finite Element Method[J]. Applied Mathematics and Mechanics, 2008, 29(7): 855-863.

## 带自由液面粘性流体运动的最小二乘有限元模拟

###### 作者简介:汤波(1982- ),男,安徽人,博士生(联系人.Tel:+86-10-62773402;E-mail:tangbo99@mails.tsinghua.edu.cn).
• 中图分类号: O357.1；O359+.1

## Viscous Flow With Free Surface Motion by Least Square Finite Element Method

• 摘要: 给出了一种求解带自由液面流体运动的数值方法．流体运动的Navier-Stokes方程应用最小二乘有限元进行离散，有限差分法用来进行时间推进．采用Lagrange方法描述网格．将模型的计算结果与二维矩形和三维圆柱形坝溃的实验结果进行了对比．计算得到的时间历程与实验结果十分吻合，验证了最小二乘有限元在此类问题中应用的可能性．
•  [1] 吕敬,李俊峰,王天舒.带弹性附件充液矩形贮箱俯仰运动动态响应[J].应用数学和力学,2007,28(3):317-327. [2] Codina R. Pressure stability in fractional step finite element methods for incompressible flows[J].Journal of Computational Physics,2001,170(1):112-140. [3] Jiang B N.The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics[M].Berlin: Springer, 1998. [4] Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian mulipliears[J].Mathematical Modeling and Numerical Analysis,1974,8(2):129-151. [5] Guermond J L, Quartapelle L.On stability and convergence of projection methods based on pressure Poisson equation[J].International Journal for Numerical Methods in Fluids,1998,26(3):1039-1053. [6] Hauashi M, Hatanaka K,Kawahara M.Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods[J].International Journal for Numerical Methods in Fluids,1991,13(7):805-840. [7] Oliver K H. Least-squares methods for the solution of fluid-structure interaction problems[D].Germany: TU Braunschweig, 2006. [8] Chang C L, Nelson J J.Least-squares finite element method for the stokes problem with zero residual of mass conservation[J].SIAM Journal on Numerical Analysis,1997,34(2):480-489. [9] Deang J M, Gunzburger M D.Issues related to least-squares finite element methods for the Stokes equations[J].SIAM Journal on Scientific Computing,1998,20(3):878-906. [10] Martin J C, Moyce W J.An experimental study of the collapse of liquid columns on a rigid horizontal plane[J].Philosophical Transactions of the Royal Society of London. Ser A, Mathematical and Physical Sciences,1952,244(882):312-324.

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##### 出版历程
• 收稿日期:  2007-11-08
• 修回日期:  2008-06-13
• 刊出日期:  2008-07-15

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