带自由液面粘性流体运动的最小二乘有限元模拟

doi:10.1007/s10483-008-0713-x

Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (7): 943-952 .doi: https://doi.org/10.1007/s10483-008-0713-x

带自由液面粘性流体运动的最小二乘有限元模拟

汤波,李俊峰,王天舒

清华大学航天航空学院，北京 100084

收稿日期:2007-11-08 修回日期:2008-06-13 出版日期:2008-07-03 发布日期:2008-01-01
通讯作者: 王天舒

Viscous flow with free surface motion by least square finite element method

TANG Bo, LI Jun-feng, WANG Tian-shu

School of Aerospace, Tsinghua University, Beijing 100084, P. R. China

Received:2007-11-08 Revised:2008-06-13 Online:2008-07-03 Published:2008-01-01
Contact: WANG Tian-shu

摘要/Abstract

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。

关键词: 粘性不可压流体, 坝溃实验, Lagrange描述, 最小二乘有限元

Abstract: A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.

Key words: Lagrangian description, dam break experiment, incompressible viscous fluid, least square finite element method

中图分类号:

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]. Applied Mathematics and Mechanics (English Edition), 2008, 29(7): 943-952 .

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 (English Edition), 2008, 29(7): 943-952 .

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带自由液面粘性流体运动的最小二乘有限元模拟

Viscous flow with free surface motion by least square finite element method

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