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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 62 , Issue 8 : 984701(2019) https://doi.org/10.1007/s11433-018-9357-0

Smoothed particle hydrodynamics (SPH) for modeling fluid-structure interactions

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  • ReceivedNov 29, 2018
  • AcceptedJan 18, 2019
  • PublishedMar 29, 2019
PACS numbers

Abstract

Fluid-structure interaction (FSI) is a class of mechanics-related problems with mutual dependence between the fluid and structure parts and it is observable nearly everywhere, in natural phenomena to many engineering systems. The primary challenges in developing numerical models with conventional grid-based methods are the inherent nonlinearity and time-dependent nature of FSI, together with possible large deformations and moving interfaces. Smoothed particle hydrodynamics (SPH) method is a truly Lagrangian and meshfree particle method that conveniently treats large deformations and naturally captures rapidly moving interfaces and free surfaces. Since its invention, the SPH method has been widely applied to study different problems in engineering and sciences, including FSI problems. This article presents a review of the recent developments in SPH based modeling techniques for solving FSI-related problems. The basic concepts of SPH along with conventional and higher order particle approximation schemes are first introduced. Then, the implementation of FSI in a pure SPH framework and the hybrid approaches of SPH with other grid-based or particle-based methods are discussed. The SPH models of FSI problems with rigid, elastic and flexible structures, with granular materials, and with extremely intensive loadings are demonstrated. Some discussions on several key techniques in SPH including the balance of accuracy, stability and efficiency, the treatment of material interface, the coupling of SPH with other methods, and the particle regularization and adaptive particle resolution are provided as concluding marks.


Funded by

the National Natural Science Foundation of China(Grant,No.,51779003)

and the National Key Research Project(Grant,No.,2018YFB0704000)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant No. 51779003), and the National Key Research and Development Project of China (Grant No. 2018YFB0704000). The authors appreciate the help from Dr. Muhammad Saif Ullah Khalid for smoothing the paper and giving constructive suggestions.


Contributions statement

These authors contributed equally to this work.


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  • Figure 1

    (Color online) Illustration of particle distribution around particle i in two-dimensional space. κhi represents the radius of the support domain S of the interested particle i.

  • Figure 2

    (Color online) Diagram of the mirror particle approach.

  • Figure 3

    (Color online) Diagram of the dummy particle approach. The dummy particles can be associated with boundary particles (a) or projectingpoints (b).

  • Figure 4

    (Color online) Illustration of moving FSI interface in SPH particle model. (a) Initial SPH particle distribution, and (b) SPH particle distribution after evolution. Interaction between particles from different materials can introduce shear and tensile stress and can prohibit sliding and separation of different materials.

  • Figure 5

    (Color online) An illustration of particle-particle contact.

  • Figure 6

    Schematic diagram of the function ψi=ψ(ki).

  • Figure 7

    (Color online) Illustration of the CD-SBT algorithm for (a) fixed and (b) moving solid boundaries.

  • Figure 8

    (Color online) (a) The attachment of SPH particles to finite elements and (b) contact force produced between SPH particles and finite elements.

  • Figure 9

    (Color online) The subarea ABCD and corresponding ghost particles in support domain of fluid particle i.

  • Figure 10

    Illustration of the EBG model. An EBG is composed of two adjacent line segments connecting three neighboring particles.

  • Figure 11

    (Color online) Particle distributions at different time instants of the liquid sloshing.

  • Figure 12

    (Color online) Pressure values at probe P1 (a) and P2 (b) during the sloshing process.

  • Figure 13

    (Color online) Pressure distribution for the liquid sloshing at simulation time t=2.2, 2.4, 2.5, 2.7, 2.9, 3.1, 3.3 and 3.6 s from (a) to (h), respectively.

  • Figure 14

    (Color online) Wave height at the probe point for liquid sloshing, (a) hw=0.6 m and T=1.3 s and (b) hw=0.5 m and T=1.875 s.

  • Figure 15

    (Color online) The water exit of a horizontal cylinder at different time instants (from (a) to (e): T=0.0, 0.6, 0.8, 1.0, 2.0 s) obtained from left: numerical results by Lin (solid line) [198], numerical results by Greenhow and Moyo (dashed line) [197], theoretical results by Tyvand and Miloh (dotted line) [199] and right: SPH results by Liu et al. [1].

  • Figure 16

    (Color online) SPH simulation snapshots [116] and experimental observations [201] for the dam break with an elastic gate. (a) T=0.0 s; (b) T=0.04 s; (c) T=0.08 s; (d) T=0.12 s; (e) T=0.24 s; (f) T=0.32 s.

  • Figure 17

    (Color online) Horizontal (a) and vertical (b) displacements of the free end of the elastic gate, and (c) time history of water level during the dam break process, obtained from SPH simulations [116] and experimental observations [201].

  • Figure 18

    (Color online) The stress distribution in elastic beam and the pressure field in fluid during the water entry process obtained using present SPH-FEM. From left to right, the simulation time is 1, 2 and 3 ms, respectively.

  • Figure 19

    (Color online) Time history of the vertical force on the beam obtained from present SPH-FEM, the semi-analytical solution [204] and the SPH-FEM results by Fourey et al. [171].

  • Figure 20

    (Color online) Comparison of SPH-EBG results [143] with the experimental results from Alben et al. [209]. The length of the rigid fiber is 2.0 cm and the length of the flexible fiber is 3.3 cm.

  • Figure 21

    Three typical bending modes of flexible fibers. (a) U-shaped mode (L=3.3 cm), (b) flapping mode (L=5.0 cm), and (c) closed mode (L=8.0 cm).

  • Figure 22

    (Color online) The streamlines and vortices of the flexible fiber with length L=8.0 cm at different times (and velocities). The time or flow velocity increases from (a) to (f), with the lines denoting streamlines and the color showing the angular velocity of SPH particles.

  • Figure 23

    (Color online) Vertical (the first and second columns) and horizontal (the third and fourth columns) velocity distributions at one time instant of single particle sedimentation. The first and third columns are obtained using the modified SPH, and the second and fourth columns are obtained using the FE-FBM.

  • Figure 24

    (Color online) Vertical velocity distribution at the dimensionless sedimentation time up: T=10 and down: T=16, obtained using the conventional SPH (left), modified SPH (middle) and FE-FBM (right).

  • Figure 25

    (Color online) Comparison of vertical positions (a) and vertical velocities (b) of two falling particles in a closed channel.

  • Figure 26

    (Color online) Distribution of the SPH points close to the upper solid boundary obtained using present SPH with (a) and without (b) artificial stress model.

  • Figure 27

    (Color online) Temperature field of the fluid at sedimentation time t=0.2, 0.6, 1.0 and 1.8 s obtained using FE-FBM (a) and FPM-PST (b) respectively, Grashof number Gr=1000.

  • Figure 28

    (Color online) Zoom in view of the temperature distribution at sedimentation time 0.6 s obtained using FPM-PST.

  • Figure 29

    (Color online) Position (a) and velocity (b) of the settling particle obtained using FE-FBM and FPM-PST with different special resolutions, Gr=1000.

  • Figure 30

    (Color online) A typical snapshot in EXW process obtained by the density-adaptive SPH. The red, black and blue particles represent the base plate, flyer plate and explosive, respectively. The nephogram in explosive represents the explosion wave.

  • Figure 31

    (Color online) Welding interfaces obtained from (a)-(c) experimental observations [231] and (d)-(f) SPH simulations [128].

  • Figure 32

    (Color online) Temperature distribution of the flyer and base plates in EXW with increasing amount of explosive from left to right.

  • Figure 33

    Shape of aluminum jet given by the SPH simulation [124] (a) and reference results [232] (b).

  • Figure 34

    (Color online) Shapes of the formed aluminum jets without (a) and with (b) surrounding aluminum case obtained by SPH simulations.

  • Figure 35

    (Color online) Comparison of the experimental radiophoto [233] (a) with the SPH simulation results (b) for the penetration process of a shaped charge.

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