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
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.
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.
Fig.3Construction of node-based partial smoothing domain
Fig.4Geometry model and meshed model of disk falling
Fig.5Vertical velocity of point A at different times
Fig.6Horizontal velocity distribution of fluid at different times
Fig.7Vertical velocity distribution of fluid at different times
Fig.8Pressure distribution of fluid at different times
Fig.9Computational 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.1Mesh 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.2Mesh setting for fluids of elastic beam in a fluid tunnel
Fig.10Horizontal displacement curves of top point A in different solid solvers
Fig.11Displacement contours of solids for three different methods
Fig.12Velocity 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.3Computational 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.4Computational 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.5Computational 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.6Computational efficiency with fluid mesh MF2
Fig.13Computational 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.7Mesh 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.8Computational 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.9Computational 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.10Computational efficiency with fluid mesh node number of 16641
Fig.14Horizontal velocity contours and streamline charts obtained by using NPS-PIM as solid solver
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