求解流固耦合问题的一种四步分裂有限元算法

王华坤; 洪国军; 杨闻宇; 喻国良

doi:10.3879/j.issn.1000-0887.2013.07.005

求解流固耦合问题的一种四步分裂有限元算法

doi: 10.3879/j.issn.1000-0887.2013.07.005

¹上海交通大学船舶海洋与建筑工程学院,上海 200240;²中交上海航道勘察设计研究院有限公司,上海 200120

基金项目: 国家高技术研究发展计划项目( 2007AA09Z312)

详细信息

作者简介:
王华坤(1985—),男,河北人,博士生 (E-mail: hkwang@sjtu.edu.cn);喻国良(1963—),男,教授,博士生导师 (通讯作者. E-mail:yugl@sjtu.edu.cn).

中图分类号: O357.1
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出版历程
- 收稿日期: 2013-03-27
- 修回日期: 2013-05-28
- 刊出日期: 2013-07-15

A Four-Step Fractional Finite Element Method for Fluid-Structure Interaction

¹School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;²Shanghai Waterway Engineering Design and Consulting Co Ltd, Shanghai 200120, P.R.China

摘要

摘要: 基于arbitrary Lagrangian Eulerian (ALE) 有限元方法，发展了一种求解流固耦合问题的弱耦合算法．将半隐式四步分裂有限元格式推广至求解ALE描述下的Navier-Stokes（N-S）方程，并在动量方程中引入迎风流线（streamline upwind/Petrov-Galerkin, SUPG）稳定项以消除对流引发的速度场数值振荡；采用Newmark-β法对结构方程进行时间离散；运用经典的Galerkin有限元法求解修正的Laplace方程以实现网格更新，每个计算步施加网格总变形量防止结构长时间、大位移运动时的网格质量恶化．运用上述算法对弹性支撑刚性圆柱体的流致振动问题进行了数值模拟，计算结果与已有结果相吻合，初步验证了该算法的正确性和有效性．
- ALE有限元 /
- 流固耦合 /
- 半隐式四步分裂 /
- 修正Laplace方程 /
- 网格更新
Abstract: A loosely-coupled algorithm for fluid-structure interaction based on arbitrary Lagrangian Eulerian(ALE) finite element method was proposed. The semi-implicit four-step fractional finite element method was extended to solve Navier-Stokes equations of ALE description, where the streamline upwind/Petrov-Galerkin (SUPG) stabilization term was added to the momentum equation to eliminate numerical oscillations of the velocity field. The temporal integration of the equation of motion for the structure was done with a Newmark-βalgorithm while the mesh updating was performed based on the modified Laplace equation solved by a standard Galerkin FEM. The entire deformation was imposed at each time step in order to avoid deterioration in mesh quality with long-term and large amplitude oscillations or deformations. The proposed method was applied to the numerical simulations on flow-induced vibrations of an elastically mounted circular cylinder with one and two degrees of freedom. Numerical results show good agreement with the existing solutions and suggest that the present method is competitive in terms of accuracy and efficiency.
- ALE finite element method /
- fluid-structure interaction /
- semi-implicit four-step fraction /
- modified Laplace equation /
- mesh updating

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参考文献(15)

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