光滑点插值法应用于流固耦合的比较研究

doi:10.3785/j.issn.1008-973X.2020.08.025

浙江大学学报(工学版)

2020, Vol. 54

Issue (8): 1645-1654 DOI: 10.3785/j.issn.1008-973X.2020.08.025

流体力学

光滑点插值法应用于流固耦合的比较研究

黄硕1(

),王双强1,王鹏1,张桂勇1,2,3,*(

)

1. 大连理工大学船舶工程学院辽宁省深海浮动结构工程实验室，辽宁大连 116024
2. 大连理工大学工业装备结构分析国家重点实验室，辽宁大连 116024
3. 高新船舶与深海开发装备协同创新中心，上海 200240

Comparative study of application of smoothed point interpolation method in fluid-structure interactions

Shuo HUANG1(

),Shuang-qiang WANG1,Peng WANG1,Gui-yong ZHANG1,2,3,*(

)

1. Liaoning Engineering Laboratory for Deep-Sea Floating Structures, School of Naval Architecture, Dalian University of Technology, Dalian 116024, China
2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
3. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China

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摘要：

针对传统有限元法（FEM）固体模型刚度过硬导致低阶单元求解精度较低的问题，采用光滑点插值方法（S-PIM）. S-PIM得益于梯度光滑技术能软化固体模型刚度，基于容易剖分的线性背景网格能改善固体求解精度. 采用不同的光滑域构建方式可以得到不同的固体求解器，从而在不同程度上提高计算精度. 本研究以浸没光滑点插值法（IS-PIM）为基础，在流固耦合（FSI）模型中采用较成熟的半隐式特征分离法（CBS）作为流体求解器，分别采用有限元法、边基光滑点插值方法（ES-PIM）以及点基局部光滑点插值方法（NPS-PIM）作为固体求解器，比较不同固体求解器条件下的计算精度和效率. 结果表明，与边基光滑点插值方法和有限元法相比，在流固耦合模型中采用点基局部光滑点插值法可以得到更准确的固体模型刚度，也更有利于计算精度和计算效率的提高.

关键词： 浸没方法; 流固耦合; 有限元法; 光滑点插值方法; 计算效率

Abstract:

The traditional finite element method (FEM) suffers the low accuracy problems for low order elements due to the overly stiffness problem in solid model. Thus, the smoothed point interpolation method (S-PIM) was employed. S-PIM has been proved to be able to soften solid stiffness through the gradient smoothing operation, and improve the accuracy of solving solid problems by using the linear background mesh, easily to be meshed. Different solid solvers can be got by different ways of constructing smoothing domains, improving the computational accuracy differently. In the framework of immersed smoothed point interpolation method (IS-PIM), the semi-implicit characteristic-based split (CBS) procedure was used as fluid solver in fluid-structure interactions (FSI) model, the performance of different solid solvers, including FEM, edge-based smoothed point interpolation method (ES-PIM) and the node-based partly smoothed point interpolation method (NPS-PIM), were compared to each other in terms of accuracy and efficiency. Results show that the NPS-PIM can get more accurate stiffness of solid model, and get better results in computational accuracy and computational efficiency comparing with ES-PIM and FEM.

Key words: immersed method fluid-structure interaction finite element method smoothed point interpolation method computational efficiency

收稿日期: 2019-04-28 出版日期: 2020-08-28

CLC:

O 357.1

基金资助: 国家自然科学基金资助项目（51639003）；中央高校基本科研业务费资助项目（DUT20TD108，DUT20LAB308）；辽宁省兴辽英才计划资助项目（XLYC1908027）

通讯作者: 张桂勇 E-mail: uheverlast@mail.dlut.edu.cn;gyzhang@dlut.edu.cn

作者简介: 黄硕（1996—），男，硕士生，从事流固耦合研究. orcid.org/0000-0002-7573-8427. E-mail： uheverlast@mail.dlut.edu.cn

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引用本文:

黄硕,王双强,王鹏,张桂勇. 光滑点插值法应用于流固耦合的比较研究[J]. 浙江大学学报(工学版), 2020, 54(8): 1645-1654.

Shuo HUANG,Shuang-qiang WANG,Peng WANG,Gui-yong ZHANG. Comparative study of application of smoothed point interpolation method in fluid-structure interactions. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1645-1654.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.08.025 或 http://www.zjujournals.com/eng/CN/Y2020/V54/I8/1645

图 1 边基光滑域构造[21]

图 2 点基光滑域构造[19]

图 3 点基局部光滑域构造[19]

图 4 圆盘沉降问题的几何模型以及网格划分模型

图 5 点A在竖直方向上的速度-时间曲线

图 6 流体在不同时刻处水平方向速度场

图 7 流体在不同时刻处竖直方向速度场

图 8 流体在不同时刻处压力场

图 9 流域内弹性梁变形问题计算模型

表 1 流域内弹性梁变形问题固体网格设置

表 2 流域内弹性梁变形问题流体网格设置

图 10 不同固体求解器下点A水平位移随时间变化的曲线

图 11 3种方法固体位移云图

图 12 采用不同固体求解器得到的速度云图和流线图

表 3 流体网格为MF1时的计算误差

表 4 流体网格为MF1时的计算时间

表 5 流体网格为MF1时的计算效率

表 6 流体网格为MF2时的计算效率

图 13 顶腔驱动流体作用于超弹性墙问题计算模型

表 7 超弹性墙问题固体网格设置

表 8 流体网格节点数为16641时的计算误差

表 9 流体网格节点数为16641时的计算时间

表 10 流体网格节点数为16641时的计算效率

图 14 采用NPS-PIM作为固体求解器得到的水平速度云图和流线图

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