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Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (8): 1645-1654    DOI: 10.3785/j.issn.1008-973X.2020.08.025
    
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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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 wordsimmersed method      fluid-structure interaction      finite element method      smoothed point interpolation method      computational efficiency     
Received: 28 April 2019      Published: 28 August 2020
CLC:  O 357.1  
Corresponding Authors: Gui-yong ZHANG     E-mail: uheverlast@mail.dlut.edu.cn;gyzhang@dlut.edu.cn
Cite this article:

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.

URL:

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


光滑点插值法应用于流固耦合的比较研究

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 
Fig.1 Construction of edge-based smoothing domain
Fig.2 Construction of node-based smoothing domain
Fig.3 Construction of node-based partial smoothing domain
Fig.4 Geometry model and meshed model of disk falling
Fig.5 Vertical velocity of point A at different times
Fig.6 Horizontal velocity distribution of fluid at different times
Fig.7 Vertical velocity distribution of fluid at different times
Fig.8 Pressure distribution of fluid at different times
Fig.9 Computational model of elastic beam in a fluid tunnel
固体网格 尺寸/cm 节点数 单元数
MS1 1/50 123 160
MS2 1/60 196 288
MS3 1/75 244 360
MS4 1/100 405 640
MS5 1/300 3133 5760
Tab.1 Mesh setting for solids of elastic beam in a fluid tunnel
流体网格 尺寸/cm 节点数 单元数
MF1 1/50 10251 20000
MF2 1/100 40501 80000
Tab.2 Mesh setting for fluids of elastic beam in a fluid tunnel
Fig.10 Horizontal displacement curves of top point A in different solid solvers
Fig.11 Displacement contours of solids for three different methods
Fig.12 Velocity contours and streamline charts obtained by using different solid solvers
求解器 固体网格
MS1 MS2 MS3 MS4
FEM 1.27×10?1 6.85×10?2 6.25×10?2 2.80×10?2
ES-PIM 3.21×10?2 1.02×10?2 1.09×10?2 6.10×10?3
NPS-PIM 7.40×10?3 4.70×10?3 3.10×10?3 2.50×10?3
Tab.3 Computational error with fluid mesh MF1
求解器 固体网格
MS1 MS2 MS3 MS4
FEM 5.26×103 5.40×103 5.48×103 5.72×103
ES-PIM 1.33×104 1.34×104 1.35×104 1.38×104
NPS-PIM 7.03×103 7.21×103 7.17×103 7.54×103
Tab.4 Computational time with fluid mesh MF1
求解器 固体网格
MS1 MS2 MS3 MS4
FEM 1.000 1.000 1.000 1.000
ES-PIM 1.566 2.695 2.327 1.902
NPS-PIM 12.844 10.909 15.410 8.490
Tab.5 Computational efficiency with fluid mesh MF1
求解器 固体网格
MS1 MS2 MS3 MS4
FEM 1 .000 1.000 1.000 1.000
ES-PIM 1.396 0.924 0.942 0.790
NPS-PIM 4.653 9.440 21.913 13.841
Tab.6 Computational efficiency with fluid mesh MF2
Fig.13 Computational model of a hyper elastic wall problem driven by lid-driven cavity flow
固体网格 尺寸/cm 节点数 单元数
MS1 1/40 1701 3200
MS2 1/50 2652 5050
MS3 1/100 10251 20000
Tab.7 Mesh setting for solids of a hyper elastic wall problem
求解器 固体网格
MS1 MS2
FEM 5.06×10?1 5.04×10?1
ES-PIM 1.58×10?1 1.57×10?1
NPS-PIM 9.06×10?3 8.30×10?3
Tab.8 Computational error with fluid mesh node number of 16641
求解器 固体网格
MS1 MS2
FEM 9.35×103 1.17×104
ES-PIM 1.79×104 2.30×104
NPS-PIM 1.26×104 1.50×104
Tab.9 Computational time with fluid mesh node number of 16641
求解器 固体网格
MS1 MS2
FEM 1.000 1.000
ES-PIM 1.672 1.622
NPS-PIM 39.086 47.235
Tab.10 Computational efficiency with fluid mesh node number of 16641
Fig.14 Horizontal velocity contours and streamline charts obtained by using NPS-PIM as solid solver
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