MPS-DEM coupling method for interaction between fluid and thin … · 2021. 7. 25. · MPS-DEM...

Ocean Engineering 236 (2021) 109449

Available online 24 July 20210029-8018/© 2021 Elsevier Ltd. All rights reserved.

MPS-DEM coupling method for interaction between fluid and thin elastic structures

Fengze Xie a, Weiwen Zhao a, Decheng Wan a,b,*

a Computational Marine Hydrodynamics Lab (CMHL), School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China b Ocean College, Zhejiang University, Zhoushan, 316021, China

A R T I C L E I N F O

Keywords: Moving particle semi-implicit method (MPS) Discrete element method (DEM) Fluid-structure interaction (FSI) Parallel technique Partition technique MPSDEM-SJTU solver

A B S T R A C T

In this present work, an in-house solver MPSDEM-SJTU is developed based on the improved Moving Particle Semi-implicit (MPS) method and Discrete Element Method (DEM). The MPS method is used to simulate the movement of the fluid while a more precise bond model, which includes the rolling contact model, is employed to analyse the dynamic responses of structures. Based on the boundary condition of MPS, a simple coupling scheme is proposed for the information exchange. The pressure carried by MPS particles is passed to the DEM particles. In turn, the velocity and displacement information will be transferred from the solid domain to the fluid domain. In order to improve the computation efficiency, the parallel technique is introduced to the solver. Be-sides, a Partition Technique (PT) is developed to avoid the misjudgment of the neighbor particles near the thin structures. The DEM-based structural solver is firstly validated for simulating an oscillating cantilever plate. Then, the coupling model is validated by comparison with benchmark tests, such as hydrostatic water column on an elastic plate, sloshing flows in a rolling tank with a thin elastic baffle, the flood discharge with an elastic gate and dam-break with an elastic plate. The numerical results show good agreement with experimental data and other numerical results. In addition, the developed solver is successfully extended to tackle FSI problems with fracture.

1. Introduction

The Fluid-Structure Interaction (FSI) problems with violent free surface flows widely exist in ocean engineering field, such as sloshing in a rolling tank with elastic baffles (Idelsohn et al., 2008a), ocean waves interacting with the sea ice floes (Zhang et al., 2019) and the water impacting the ship bottom plate (Stenius et al., 2011). The fluid dy-namics applied by severe flows may lead to large deformations and even fractures of structures. Therefore, it is necessary to investigate the FSI problems for the safety of the offshore structures. Although the experi-mental technologies have developed maturely and reliably, these still have some unavoidable drawbacks. Experiments are usually time and money consuming. In addition, sometimes the experimental model sizes are much smaller than the actual sizes of objects. Therefore, the accu-racy of the experimental data may be affected due to the scale effect. The numerical technique has developed fast in the past years and gradually formed complementary relationship with experimental techniques.

According to the treatment for interface of fluids and structures, the numerical techniques for FSI problems can be divided into two main categories (Hwang et al., 2014): the monolithic and the partitioned approaches. For the former, the fluid movement and the structure re-sponses are solved with one system of governing equations. For the latter, the fluids and the structures are treated separately and the in-formation is exchanged through the interpolation. Although the errors exist during the interpolation procedure, the partition approaches are more simplified and flexible for the complex FSI problems, which has attracted more attention of researchers. Considering the advantages of different methods for fluid and structure solution, many coupling methods have been proposed for FSI problem.

The grid-based methods are the mainstream approaches to simulate the flow field. The high-order schemes and the parallel strategy can be easily introduced to the grid-based methods, which can enhance the accuracy and efficiency of these methods. The low accuracy and poor stability of the particle-based methods always bothered the researchers

* Corresponding author. Computational Marine Hydrodynamics Lab (CMHL), School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China.

E-mail address: [email protected] (D. Wan).

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Ocean Engineering

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https://doi.org/10.1016/j.oceaneng.2021.109449 Received 7 May 2021; Received in revised form 21 June 2021; Accepted 3 July 2021

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and many corrective methods have been proposed to overcome those drawbacks. Tanaka and Masunaga (2010) proposed a mixed source term for the Poisson Pressure Equation (PPE) and a gradient model of mo-mentum conservation. Khayyer and Gotch (2010, 2011, 2012) did a

series of work to improve the accuracy and stability of particle-based methods. High-order schemes were proposed for Laplacian model, source term of Poisson Pressure Equation (PPE) and gradient model of MPS. Considering the errors bringed by the uneven distribution and the aggregation of the particles, the optimized particle shifting scheme was also proposed by Khayyer et al. (2017). Compared with traditional grid-based methods, the particle-based method shows its advantages in capturing complex free surface, especially for fragmentations and splashing. Besides, the structures with large deformation and movement are hard to handle, which may cause the distortion of the grids. The distorted grids affect the accuracy of simulation and the mesh recon-struction is computationally expensive. In the contrast, it is easy for particle-based methods to overcome these drawbacks. There are no fixed topological relationships among lagrangian particles and the informa-tion exchange is not restricted to specific nodes. Therefore, the particle methods have the potential to be applied to the severe FSI problems.

In recent years, many structural analysis methods have been coupled with particle methods to investigate FSI problems. Yang et al. (2012) coupled Smoothed Particle Hydrodynamics (SPH) method with Finite Element Method (FEM). The accuracy of coupling method was verified by comparison with the benchmark tests, such as the sloshing with elastic baffle and flood discharge with elastic gate. Khayyer et al. (2018a)) employed projection-based Incompressible SPH (ISPH) method for simulation of fluid and developed a novel SPH-based struc-ture model. The Fluid-Structure Acceleration-based (FSA) or the Pres-sure Integration (PI) coupling schemes were compared in detail, The ISPH-SPH method was applied for the water entry of elastic wedge and panel. (Khayyer et al. (2021b)) further developed an ISPH-HSPH solver for simulation of fluid interacting with composite structures. A Hamiltonian SPH (HSPH) was developed for the structure analysis. Falahaty et al. (2018) coupled Moving Least Squares (MLS) method and Dual Particle Dynamics (DPD) structure model with Moving Particle Semi-implicit (MPS) method, respectively. The MLS-MPS model and DPD-MPS model were systematically compared through a series of nu-merical simulations. Chen et al. (2019) developed an in-house 3-D FSI solver MPSFEM-SJTU based on MPS method and FEM. A Kernel Function-Based Interpolation (KFBI) was introduced to handle the in-formation exchange between MPS boundary particles and FEM grids. The 3-D sloshing in the tank made of elastic material was investigated. Hu et al. (2019) coupled SPH and Smoothed Point Interpolation Method (SPIM) to simulate the sloshing in the tank with elastic baffle. There was not a consistent one-to-one match between SPIM nodes and SPH ghost particles. Physical qualities, such as velocity, displacement and force, are exchanged using interpolation. Long et al. (2016) introduced a particle-element algorithm to ISPH-FEM and SPH-FEM. Through some typical simulations, the effectiveness of this algorithm was proved. Zhang et al. (2020) used Decoupled Finite Particle Method (DFPM) and Smoothed FEM (SFEM) to study the effect of the configuration of elastic baffles to the sloshing. The virtual particle strategy was adopted to treat

Fig. 1. Bonded-particle model with rolling contact model.

Fig. 2. Arrangement of particles.

Fig. 3. Coupling strategy for MPS-DEM.

Fig. 4. Sketch of free-surface detection.

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the interaction between the fluid and structures. Yang and Zhang (2018) used MPS method coupling with Large Eddy Simulation (LES) methods to study the interaction between the dam break flows and elastic baffles.

Although both the fluid domain and elastic structures were modelled by MPS methods, the partitioned approach was adopted for the coupling.

Discrete Element Method (DEM) as another lagrangian-particle

Fig. 5. Sketch of the neighbor particle search near the thin structure.

Fig. 6. Sketch of the fracture process.

Fig. 7. Diagram of domain decomposition (MPS part).

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based method can be used to describe the interaction among the solid bodies and has been widely applied to the engineering and nature field, including the particle flows (Sakai et al., 2012), multi rigid body inter-action (Canelas et al., 2016), deformation and fracture of structures (Wu et al., 2016; 2018). The real ocean environment is more complicated, which includes interactions among fluids, particles and structures.

Compared with the solid part of afore-mentioned FSI methods, DEM has the potential to tackle more complex ocean problems. The response of elastic structures was usually simulated by DEM with Bonded Particle Model (BPM), which was firstly proposed by Potyondy and Cundall (2004). The moment induced by relative rotation between neighbouring DEM particles is calculated through Hooke’s law. Jiang et al. (2005) introduced a rolling contact model to the traditional bond model, which assumed that there were countless springs in the bond between two neighbouring particles. The basic concept of rolling contact model is similar with the BPM. The rolling contact model was further modified to suit for the situation with large relative rotation by Wang (2020). Be-sides, the force–displacement contact law of DEM was replaced by stress–strain form. The new bond model was successfully applied to simulate the large deformation and fracture of elastic structures. Zhao (2015) adopted only two subnormal springs to transmit a moment be-tween two neighbouring particles.

Several particle-based methods have been coupled with DEM to investigate the FSI problems. There are two main models (7-disc and 9- disc) for structures according to the arrangement of DEM particles (Owen et al., 2020). Tang et al. (2018) coupled SPH and DEM for the FSI problems. Neighbouring DEM particles was joined together by two parallel springs, which was a simplified version of rolling contact model. For the stability of the structure, DEM particles were arranged as a hexagonal scheme (7-disc). However, it is difficult to configure SPH boundary particles. Sun et al. (2019a) adopted 9-disc arrangement of

Fig. 8. Diagram of domain decomposition (DEM part).

Fig. 9. The sketch of the model: an oscillating cantilever plate.

Table 1 Parameters in the simulation of an oscillating cantilever plate.

DEM parameters Values

DEM particle diameter (m) 5 × 10− 3, 4 × 10− 3, 2.5 × 10− 3

DEM particles number 164, 255, 648 Material density (kg/m3) 1000 Plate Young’s modulus (MPa) 2 Plate Poisson ratio 0.4 DEM time step (s) 1 × 10− 6

Fig. 10. Comparison of displacement time histories between analytic solution and numerical results with different particle sizes - an oscillating canti-lever plate.

Table 2 The results obtained by different methods in the simulation of an oscillating cantilever plate.

No-dimensional period (Tc0/L)

No-dimensional amplitude (A/L)

Analytic solution 72.39 0.115 Hwang et al.

(2014) 72.4 0.113

Antoci et al.(2007) 81.5 0.124 Gray et al. (2001) 82 0.125 Present (d =

0.0025) 71.8 0.113

Present (d = 0.004) 73.2 0.115 Present (d = 0.005) 74.4 0.118

Fig. 11. The distribution of the stress at t = 0.57s - an oscillating canti-lever plate.

F. Xie et al.


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DEM particles and the BPM. The MPS-DEM method was used to inves-tigate the influence of dam break flows to a floating deformable struc-ture with moorings. A more precise bond model containing the rolling contact model (Jiang et al., 2005) is used to simulate the structural response in MPSDEM-SJTU solver. The coupling schemes of MPS/SPH with DEM are not showed in detail in those works mentioned above. In present work, a simple coupling scheme is proposed and its stability and accuracy are checked in detail. Besides, the stress field is presented in the structure of DEM, by which the area where its structure is prone to damage can be easily detect. In addition, some marine structures are very thin such as the ship hull shell and the hydraulic turbine blade. The fluid on both sides of the thin structures will not interfere with each other. The interaction between fluid and thick structures or the fluid only acting on one side of the structure can be simulated by previous SPH-DEM and MPS-DEM models. However, the effect of thin structures to the neighbor particle search have rarely been considered or mentioned. To offset this vacancy, a Partition Technique (PT) is estab-lished and implanted into the in-house MPSDEM-SJTU solver. Due to the more accurate neighbouring particles search, the force exerted on the structures is more accurate.

The elastic structures tend to be thin and the corresponding wall

particles should be small. Therefore, the total amount of particles will be large in the whole region with single-resolution. In order to improve the computational efficiency, many approaches have been introduced to particle methods. Those approaches can be classified as multi-resolution techniques, parallel technique and GPU acceleration technique. For multi-resolution techniques, the particles with small spacing are only arranged at the field that needs be focused on, which reduces compu-tational load and meets the requirements of local accuracy. Sun et al. (2019b) investigated a violent fluid-structure dam-break problem with multi-phase δ-SPH methods and Adaptive Particle Refinement (APR). The APR region was set around the elastic structure and the coarse particles were splitted into more fine particles when they entered the refinement region. Khayyer et al. (2018b, 2021a) firstly introduced a multi-resolution method into MPS and ISPH-SPH methods to solve the hydro-elastic FSI problem. The elastic baffle was simulated by fine particles while the flow field was composed of coarse particles. The key idea of parallel technique is to divide tasks into several parts and assign them to different CPU processors for processing at the same time. Mar-rone et al. (2012) developed a parallel 3-D SPH model, which achieves a high parallel efficiency. The wave pattern generated by a moving ship is successful captured. As a new hardware, GPU is in possession of more Arithmetic Logic Units (ALU) than CPU. Therefore, GPU can achieve high Floating Point Operations Per Second (FLOPS) and deal with large

Fig. 12. The sketch of model: the hydrostatic water column on an elastic plate.

Table 3 Parameters in the simulation of the hydrostatic water column on an elastic plate.

MPS parameters Values DEM parameters Values

Initial particle spacing (m)

1.25 ×10− 2

DEM particle diameter (m)

1.25 ×10− 2

MPS particles number 14396 DEM particles number 324 Fluid density (kg/m3) 1000 Material density (kg/m3) 2700 Fluid viscosity (Pa⋅s) 8.9 × 10− 5 Gate Young’s modulus

(GPa) 67.5

MPS time step (s) 1 × 10− 3 Gate Poisson ratio 0.34 Total time (s) 10 DEM time step (s) 1 × 10− 7

Fig. 13. Vertical displacement time histories at the midpoint of the elastic plate. (a) Comparison of results obtained by MPS-DEM with different particle sizes and analytic solution. (b) Comparison of results obtained by SPH-FEM (Li et al., 2015), ISPH-SPH (Khayyer et al., 2018a), SPH-SPIM (Hu et al., 2019), MPS-DEM and analytic solution - hydrostatic water column on an elastic plate.

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amounts of data simultaneously (Chen and Wan, 2019a). Chen and Wan (2019b) introduced GPU acceleration technique to MPS method and the speed-up ratio can be up to 25–33 times compared with single CPU. However, GPU acceleration technique is not used as widely as multi-CPU parallel technique. In this paper, the multi-CPU parallel technique is introduced to the MPS-DEM method, which also lays a foundation for the application of multi-GPU parallel technique in large-scale flow simulation.

In present study, an in-house parallel solver MPSDEM-SJTU based on MPS method and DEM is developed to simulate FSI problems. Firstly, the improved MPS method, the DEM method, the MPS-DEM coupling scheme, the parallel strategy and Partition Technique (PT) are presented briefly. In the section of numerical simulations, an oscillating cantilever plate is simulated to validate the DEM part of developed solver. Then, several numerical examples, including the hydrostatic water column on an elastic plate, the flood discharge with an elastic gate, sloshing flows in a rolling tank with a thin elastic plate and dam-break with an elastic plate, are carried out to test the accuracy and performance of the MPSDEM-SJTU solver. The parallel efficiency, the convergency and the energy conservation properties of the MPS-DEM solver are tested in the hydrostatic case. In the cases with thin elastic structures, the superiority of the PT for the neighbouring particles search near the thin structures is presented. Finally, the MPSDEM-SJTU solver is successfully extended to simulate the FSI with fracture.

2. Numerical method

2.1. MPS method for fluid simulation

MPS method was firstly proposed by Koshizuka and Oka (1996) for simulation of viscous incompressible fluid. The governing equations of the fluid consist of mass conservation equation and momentum con-servation equation, given by,

∇ ⋅ u⇀= 0 (1)

Du⇀

Dt= −

1ρ∇P+ ν∇2 u⇀ + g⇀ (2)

where the u⇀, t, ρ, P, ν and g⇀ are the velocity vector, time, fluid density,

pressure, kinematic viscosity of the fluid and gravity acceleration vector, respectively.

The interaction among MPS particles controlled by kernel function. In order to avoid the singular point, the kernel function introduced by Zhang and Wan (2012a) is employed here.

W(r)=

⎧⎨

⎩

re

0.85r + 0.15re− 1 0 ≤ r < re

0 re ≤ r(3)

where r is the distance between two particles and re is the radius of the particle interaction.

The particle interaction models contain gradient model, divergence model and laplacian model, defined as,

<∇φ>i =dn0

∑

j∕=i

φj + φir

⇀j − r⇀i|

2

⎛

⎝r⇀j − r⇀i

⎞

⎠ ⋅ W

⎛

⎝

r⇀j − r⇀i

⎞

⎠ (4)

<∇ ⋅ V⇀>i =

dn0

∑

j∕=i

(

u⇀j − u⇀i

)

⋅(

r⇀j − r⇀i

)

r

⇀j − r⇀i|

2W

⎛

⎝

r⇀j − r⇀i

⎞

⎠ (5)

<∇2φ>i =2dn0λ∑

j∕=i

(φj − φi

)

⋅ W

(r⇀j − r⇀i

)

(6)

where φ is a physical quantity, d is the number of space dimension, n0 is the initial particle density, r⇀ is the position vector relative to origin, λ is a parameter to make the increase of variance equal to the corresponding analytical solution (Koshizuka and Oka, 1996), given by,

λ=

∑

j∕=iW(r

⇀j − r⇀i

)

⋅r

⇀j − r⇀i|

2

∑

j∕=iW(r

⇀j − r⇀i

) (7)

Pressure information carried by MPS particles is obtained by solving the Pressure Poisson Equation (PPE). In order to balance between sta-bility and accuracy, a mixed source method (Khayyer and Gotoh, 2011; Tanaka and Masunaga, 2010) is adopted, defined by,

< ∇2Pk+1>i = (1 − γ)ρΔt∇⋅u⇀

*i − γ

ρΔt2

< n*>i − n0

n0 (8)

where Pk+1, Δt, u⇀*i and n* are the pressure of the step k+ 1, time step,

temporal velocity and temporal particle density. γ is a blending parameter, whose value is set to be 0.01 in this paper.

2.2. DEM method for structure simulation

In classical DEM method, the solid body is made of particles. The motion of the particle is governed by Newton’s second law, expressed as,

mDv⇀

Dt=F

⇀c + mg⇀ + F

⇀int(9)

IDω⇀

Dt=M

⇀ t

c (10)

where m and I are the mass and the moment of inertia, v⇀ and ω⇀ are the

linear and angular velocity, F⇀

c and Mtc are the contact force and contact

moment among solid particles, F⇀int

is the hydrodynamics exerted on the solid particles.

The contact force is calculated based on the contact model, which consists of springs, dashpots and sliders. The DEM particles are regarded

Fig. 14. Simulation snapshot obtained by MPS-DEM at t = 0.8 s (T/dp = 5) - hydrostatic water column on an elastic plate.

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Fig. 15. Time histories of, (a) elastic strain energy of structure, (b) gravitational potential energy of structure, (c) kinetic energy of structure, (d) total energy of structure field, (e) kinetic energy of fluid, (f) gravitational potential energy of fluid, (g) total energy of fluid field, (h) total energy of the whole system and (j) normalized total energy of the whole system. (k) Normalization for total energy minus fluid kinetic energy - hydrostatic water column on an elastic plate.

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as soft spheres and they can overlap with each other. The overlap is

equal to the deformation of the springs. The contact force F⇀

c can be

decomposed into the normal component F⇀n

c and tangential component

F⇀t

c. Both components consist of elastic force and damping force.

Fnc = − kn δ

⇀n− dnΔv⇀

n(11)

F⇀t

c =

⎧⎪⎨

⎪⎩

− kt δ⇀t

− dtΔv⇀t (

F

⇀t

c

< μ

F

⇀n

c

)

− μF

⇀n

c

⋅Δv⇀

t/|Δv⇀

t|(F

⇀t

c

≥ μ

F

⇀n

c

) (12)

where k, d, δ⇀

and Δv⇀ is the stiffness, damping coefficient, relative

displacement and relative velocity. μ is the friction coefficient. μF⇀n

c

is

the boundary of the transition from static friction to dynamic friction. Fig. 1 shows the bonded-particle model (BPM) (Potyondy and Cun-

dall, 2004) with rolling contact model (Jiang et al., 2005). The DPM consists of springs and dashpots.

The particles of the structure are packed in cubic form. Based on the

beam theory, the stiffness kn can be calculated as,

kn =AEL

=tLEL

= Et = E (13)

where E is the Young’s modulus of the material. A, t and L are the cross- sectional area, thickness and length of beam element. In 2-D case, the thickness is the unit thickness.

The stiffness of spring in Tangential direction can be estimated as,

kt ≈ νkn (14)

where ν is the Poisson ratio. The damping coefficient in normal and tangential direction can be

calculated as (Wu et al., 2016),

dn = 2βnmkn

√(15)

dt = 2βtmkt

√(16)

where βn and βt are parameters, which are set to 0.2. The moment in the BPM is not only induced by the contact force in

tangential direction but also caused by the relative rotation between two

neighbouring DEM particles. The moment M⇀t

c induced by contact force in tangential direction is calculated as,

M⇀ t

c = − R⇀× F

⇀t

c (17)

In order to transfer the moment caused by relative rotation between the DEM particles, the single spring in normal direction should be equivalent to countless springs with same stiffness k

n= kn/(2R). These

Fig. 16. The percentage of the computation time for different parts of MPS- DEM - hydrostatic water column on an elastic plate.

Fig. 17. The speed-up ratio of the MPS-DEM simulation - hydrostatic water column on an elastic plate.

Fig. 18. The sketch of the model: the flood discharge with an elastic gate.

Table 4 Parameters in the simulation of the flood discharge with an elastic gate.



1 × 10− 3 DEM particle diameter (m) 1 × 10− 3


(MPa) 12

MPS time step (s) 1 × 10− 4 Gate Poisson ratio 0.4 Total time (s) 0.4 DEM time step (s) 1 × 10− 6

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springs distribute uniformly between two particles. The calculation of

moment M⇀r

c is similar to the integral in (Wang, 2020), given by,

M⇀r

c = − 2∫ R

0r(rΔθ)

(kndr

)= − 2

/

3knR3Δθ (18)

where R is the radius of DEM particle and Δθ is the relative angle be-tween the neighbouring DEM particles.

2.3. Coupling of MPS and DEM

In our previous study (Chen and Wan, 2019a), multilayer MPS par-ticles are configured on the boundary. Pressures of wall particles, which is near the fluid domain, are solved by PPE. Fig. 2 shows the arrange-ment of particles in this work. fluids and solids are discretized at the same resolution. Therefore, DEM particles overlap with MPS boundary particles. These particles of the structure exhibit properties of both MPS and DEM. A simple coupling scheme coupling scheme is proposed in this study. The pressure of the wall particles can be obtained by solving PPE, just like the fluid particles. Then, the pressure is transferred from MPS wall particles to corresponding DEM particles. The motion of DEM particles follows the force–displacement rather than stress–strain law. Therefore, the hydro-force applied on each DEM particle is focused. The

Fig. 19. Comparison of the discharge flood between experimental snapshots (Antoci et al., 2007) and numerical results - flood discharge with an elastic gate.

Fig. 20. Comparison of displacement time histories between the results ob-tained by experiment (Antoci et al., 2007) and MPS-DEM - flood discharge with an elastic gate.

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hydro-force applied to the DEM particles can be calculated as,

F⇀int

= − p⋅Δx⋅n⇀ (19)

where p is the pressure of the corresponding MPS wall particle, Δx is the distance between the MPS particles, n⇀ is the normal direction.

The information of position and the velocity are transmitted from DEM particles to MPS boundary particles.

x⇀b = x⇀s (20)

u⇀b = v⇀s (21)

The sizes of time step for MPS and DEM are quite different. Due to the explicit scheme, the time step size of DEM commonly is set to a small value. Correspondingly, a much larger time step for MPS is adopted in order to keep the stability and efficiency of the coupling algorithm. Fig. 3 shows the coupling strategy of MPS and DEM. The DEM iterates k times in one MPS iteration loop.

The MPS time-step Δtmps should meet the Courant-Friedrichs-Lewy (CFL) condition, given by,

umaxΔtmps

Δl0< C (22)

where umax is the maximum velocity of the fluid, Δl0 is the initial MPS particle spacing, C is the Courant number.

Fig. 21. Comparison of the water level at x = 0.5 m between the results ob-tained by experiment (Antoci et al., 2007) and MPS-DEM - flood discharge with an elastic gate.

Fig. 22. The sketch of the model: sloshing flows in a rolling tank with a thin elastic plate.

Table 5 Parameters in the simulation of sloshing flows in a rolling tank with a thin elastic plate.



1.0 ×10− 2

DEM particle diameter (m) 1.0 ×10− 2

MPS particles number 75662 DEM particles number 324 Fluid density (kg/m3) 997.0 Material density (kg/m3) 1100 Fluid viscosity (Pa⋅s) 5 × 10− 5 Plate Young’s modulus

(MPa) 6.0

MPS time step (s) 1 × 10− 4 Plate Poisson ratio 0.45 Total time (s) 8.0 DEM time step (s) 1 × 10− 6

Fig. 23. Comparison of the sloshing flows pattern between experimental snapshots (Idelsohn et al., 2008a) and numerical results - sloshing flows in a rolling tank with a thin elastic plate.

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The DEM time step Δtdem is decided by the mass and the stiffness of the DEM particle, defined by,

Δtdem ≤

mk

√

(23)

2.4. Free-surface detection

Based on the asymmetric distribution of neighbouring particles near the free surface, Zhang and Wan (2012b) proposed an improved surface particle detection method, whose basic concept is similar to that pro-posed by Khayyer et al. (2009). The surface particle detection method can effectively and accurately distinguish free surface particles from other particles. Fig. 4 shows the sketch of free-surface detection. The detection criterion is given by,

< n>*i < βn0 (24)

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

< F⇀>i =

dn0

∑

j∕=i

1r

⇀i − r⇀j

(

r⇀i − r⇀j

)

W(r

⇀j − r⇀i

)

<

F

⇀>i > α

F

⇀0

(25)

where F⇀

is a vector which represents the asymmetry distribution of

neighbouring particles. F⇀

0 is the F⇀

of the internal fluid particles at initial time. Parameters β and α are set to 0.8 and 0.9, respectively.

2.5. Neighbor particle search near the thin structure

Both the wall particles and fluid particles participate in the solution of the PPE. Fig. 5 presents the sketch of the neighbor particles search near a very thin plate. The fluid particles and wall particles on one side of the plate can be regarded as the neighbor particles of the particles on the other side of the plate, which is not in accordance with the actual situation and affects the accuracy of the force calculation on the plate. Therefore, it is necessary to prevent the particles on the one side of the plate become the neighbor particles of the particles from the other side. Additional judgement is added to the solver, the basic concept can be founded in Fig. 5. The centers of two neighbor ghost particles are con-nected with grey lines. If the connection (red line) of two neighbor particles intersects with one of the grey lines, they are removed from the list of neighbor particle.

2.6. FSI with fracture

The maximum tensile stress σmax of the beam element can be derived as,

σmax =− F

⇀n

c

A+

k

nRΔθ (26)

The commonly-used criterion, the Mohr-Coulomb (MC) (Wang, 2020), for the fracture induced by the shear stress is given by,

Fig. 24. Comparison of displacement time histories between results obtained by the experiment (Idelsohn et al. 2008a), MPS-DEM without PT and MPS-DEM with PT - sloshing flows in a rolling tank with a thin elastic plate.

Fig. 25. Comparison of pressure time histories between results obtained by the MPS-DEM without PT and the MPS-DEM with PT - sloshing flows in a rolling tank with a thin elastic plate.

Fig. 26. The sketch of model: dam-break with an elastic baffle.

Table 6 Parameters in the simulation of the dam-break with an elastic baffle.




MPS particles number 12989 DEM particles number 246 Fluid density (kg/m3) 1000 Material density 2500 Fluid viscosity (Pa⋅s) 8.9 ×

10− 5 Baffle Young’s modulus (MPa)

6

MPS time step (s) 2 × 10− 4 Baffle Poisson ratio 0.1 Total time (s) 0.7 DEM time step (s) 2 × 10− 6

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τcrit =C + μ

⎛

⎝F⇀n

c

A−

k

nRΔθ

⎞

⎠ (27)

If the maximum stress exceeds the criterion, the bonds are judged to be invalid and the neighbouring particles won’t re-bond again. {|σmax| > |σcrit|

|τ| > |τcrit|(28)

where τ is the shear stress in the bond. σcrit and τcrit are the ultimate stress of fracture, tensile strength and cohesion strength.

In the FSI problems with fracture, the fluid may interact with the fracture surface. Therefore, it is necessary to change the type of the MPS boundary particles as shown in Fig. 6. Once the bond of the DEM particle is broken, the corresponding MPS ghost particle will become the wall particle.

Fig. 27. Comparison of dam-break flows pattern between the MPS-FEM results (Mitsume et al., 2014) (first row) and the MPS-DEM results (second row and third row) - dam-break with an elastic baffle.

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2.7. High performance strategy for MPS-DEM

MPS particles have no topological relationship and can move freely with the fluid flows. Compared with traditional grid-based method, it is difficult to divide the whole MPS calculational domain into sub-domains of different processes. The MPS particles may transfer from one sub- domain to another. If the calculation domain is divided equally, the

difference in the number of particles between different subdomains may be too large, which directly decrease the parallel efficiency. A back-ground grid method has been introduced to particle method. The background grids (Marrone et al., 2012) cover the whole calculation domain and serve two main purposes: providing the reference frame for MPS particles to find their neighbors and allocating the nearly equal number particles to different processes to achieve the load balance. The concept of parallel strategy for the MPS is presented in Fig. 7. The size of the sub-domain will change with the movement of MPS particles to make the number of the particles in processes remain approximately constant. The cells near other processes belongs to buffer, in which the information of adjacent processes exchanges. The particles in the buffers not only simulate the flows in the local process, but also provide boundary support for the adjacent processes. The information carried by the MPS particles of elastic structures also should be broadcast to all processors after every MPS step.

If the structure fracture doesn’t occur, the neighbors of each DEM particle will not change. Therefore, the process of particle search, which is the most time-consuming step, only takes place in the first-time step. Because the DEM particles won’t transfer from one process to another as the MPS particles, the background grids, which are used in the MPS method, is unnecessary for the structure analysis. Fig. 8 shows the domain decomposition of the DEM part. A continuous beam is simply divided into four equal parts. The particles close to other processes is in the buffer region, where the information is exchanged.

3. Numerical simulations

3.1. Validation of DEM solver for structure dynamic analysis

The DEM solver is firstly used to simulate an oscillating cantilever plate. Fig. 9 shows the sketch of the model. The cantilever plate is 0.2 m long and 0.02 m thick. At the beginning, the plate without deformation is in the equilibrium position and the initial vertical velocity distribution of the plate is given by,

vy(x)= vy(L)c0f (x)f (L)

(29)

f (x) = (cos(kL) + cosh(kL))(cosh(kx) − cos(kx))+(sin(kL) − sinh(kL))(sinh(kx) − sin(kx)) (30)

where vy(L) = 0.01 is the initial vertical velocity at the free end of the plate. kL is set to 1.875 for the fundamental mode. c0 is the velocity of sound, which is decided by the properties of the material, given by,

c0 =Ks/ρs

√(31)

where Ks = 3.25 × 106N/m2 is the bulk modulus. ρs = 1000kg/m3 is the density of the plate.

Parameters of the simulation are presented in Table 1. Fig. 10 shows time histories of free end displacement of the plate. It can be noted that results of simulations with different resolutions all agree well with the analytic solution, showing good convergency performance of present solver. The results obtained by different method are listed in Table 2. Results obtained by the present solver and by Hwang et al. (2014) are close to the analytic solution than those by other researchers.

Fig. 11 presents the stress distribution of the cantilever plate at t =0.57s, which is smooth and consistent with the deformation.

3.2. Hydrostatic water column on an elastic plate

The convergence, efficiency and stability of the MPSDEM-SJTU solver are investigated by the benchmark test of a hydrostatic water column on an elastic plate. The sketch of the model is presented in Fig. 12. The water column is 2 m high and 1 m wide, which is confined in a tank. The bottom of the tank is 0.05 m thick and made of elastic

Fig. 28. Comparison of displacement time histories among results obtained by MPS-DEM, PFEM (Idelsohn et al., 2008b), SPH (Liu et al., 2013) and MPS-FEM (Mitsume et al., 2014) - dam-break with an elastic baffle.

Fig. 29. The sketch of model: dam-break with a thin elastic plate.

Table 7 Parameters in the simulation of dam-break with a thin elastic plate.




MPS particles number 87885 DEM particles number 360 Fluid density (kg/m3) 1000 Material density (kg/m3) 1161.54 Fluid viscosity (Pa⋅s) 8.9 × 10− 5 Gate Young’s modulus

(MPa) 3.5

MPS time step (s) 1 × 10− 4 Gate Poisson ratio 0.45 Total time (s) 1.0 DEM time step (s) 1 × 10− 6

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material. Table 3 shows detailed parameters of the simulation. This case has been simulated by SPH-FEM (Li et al., 2015), ISPH-SPH

(Khayyer et al., 2018a) and SPH-SPIM (Hu et al., 2019). Fig. 13 shows the time history of the mid-point displacement of the elastic plate ob-tained by different numerical methods and analytic solution. Deforma-tion trends to be stable after some initial oscillations. It can be observed

that the time history curve obtained by MPS-DEM is smoother than that obtained by SPH-FEM (Li et al., 2015) and closer to the analytic solution, which implies that present solver is more stable. Additional simulations with T/dp being 4 and 5 are also conducted. Fig. 13 shows the results with different resolutions. It can be noticed that those results are consistent showing the good convergent property of present coupling

Fig. 30. Comparison of impacting flows pattern between the experiment (Liao et al., 2015) and MPS-DEM - dam-break with a thin elastic plate.

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method. It is noted that the pressure and stress field obtained by this solver are smooth and stable as shown in Fig. 14.

The energy conservation features in the whole FSI system (Khayyer et al., 2018a; Zhang et al., 2021) of MPSDEM-SJTU solver is

investigated. The formulations of energy are given by,

ET =EFT + ES

T (32)

EST =ES

K + ESP + ES

E (33)

EFT =EF

K + EFP (34)

where ET , EFT and ES

T are the total energy of whole FSI system, fluid field and structure field, respectively. EF

K and EFP are the kinetic energy and

gravitational potential energy of fluid field. ESK, ES

P and ESE are the kinetic

energy, gravitational potential energy and elastic strain energy of structure field. The elastic strain energy of the bond model of DEM is calculate as,

ESE =ES

ETC + ESES + ES

EM (35)

ESETC =

12kn|δ

⇀n|2 (36)

ESES =

12ks|δ

⇀s|2 (37)

ESEM = 2

∫ R

01/

2(rΔθ)(rΔθ)(

kndr)= 2/

3knR3(Δθ)2 (38)

where ESETC, ES

ES and ESEM are the strain energy caused by tension/

compression force in normal direction, shear force and the moment induced by relative rotation.

The time histories of energy components in the FSI system are pre-sents in Fig. 15. It can be noted that, although there are some oscillations in the initial stage, all the energy components, except the kinetic energy of the fluid, reach almost constant values before t = 1s. From Fig. 15 (g) and (j), the normalized total energy of the whole system decreases with the drop of fluid kinetic energy, which indicates that the fluid kinetic energy takes mainly responsibility for the loss of total energy. The normalized total energy and fluid kinetic energy reach constant values before t = 10 s. The loss of normalized total energy is about 0.025% at t = 1 s and 0.054% at t = 10 s. In order to further eliminate the influence of fluid kinetic energy, the time history of normalization for total energy minus fluid kinetic energy is also presented in Fig. 15 (k). After some initial oscillations, the normalization for total energy minus fluid kinetic energy is maintain almost a constant value, which implies that the drop of fluid kinetic energy doesn’t caused by the energy exchange between structure and fluid. The drop of fluid kinetic energy may because the pressure of the fluid field oscillates slightly and the velocity of fluid is not equal to zero at initial stage. In general, MPSDEM-SJTU solver has the characteristics of energy conservation.

The parallel efficiency of MPSDEM-SJTU is tested in this case. It should be noted that the MPSDEM-SJTU solver runs on the High Per-formance Computing (HPC) cluster of CMHL group (CPU of Intel Xeon E5-2680 v2 10 Cores × 2.80GHz/node and RAM 64 GB). The percent-ages of the computation time for MPS part and DEM part are presented in Fig. 16. It can be noted that the DEM part takes up nearly half of the total computation time. This is a hydrostatic problem, so the MPS part of the solver has good stability and robustness even it runs with a larger time step. The stiffness of the elastic plate is very large. In order to meet the accuracy requirements, the time step of DEM is relatively small. Fig. 17 shows the speed-up ratio of the MPS-DEM simulation. It can be noticed that the efficiency is improved obviously when the number of GPUs is less than 4 and an efficiency of 70.6% is achieved when the solver runs on 4 CPUs. However, the efficiency is not further improved when the number of CPUs reaches 6. That because the particles number of 2-D simulation is small and the communication time between CPUs takes a large proportion of the whole simulation time. In the future work, the MPSDEM-SJTU solver will be further developed to solve 3-D FSI problems and the parallel technique will play a greater role.

Fig. 31. Comparison of displacement time histories of the free end of the thin elastic plate obtained by experiment (Liao et al., 2015), FSI-SPH (Sun et al., 2019b) and MPS-DEM - dam-break with a thin elastic plate.

Fig. 32. The sketch of model: fluid-structure interaction with fracture.

Table 8 Parameters in the simulation of FSI with fracture.





(MPa) 30

MPS time step (s) 1 × 10− 4 Gate Poisson ratio 0.4 Total time (s) 0.4 friction coefficient 0.58 - - tensile strength (Pa) 2 × 105

- - cohesion strength (Pa) 1 × 105

- - DEM time step (s) 1 × 10− 6

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Fig. 33. Simulation snapshots of FSI with fracture.

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3.3. Flood discharge with an elastic gate

In this section, a benchmark test carried out by Antoci et al. (2007) is selected to validate the accuracy of present solver. The sketch of the model is showed in Fig. 18. The water is placed at the right side and an elastic gate is hung on the rigid wall. The water column is 0.1 m wide and 0.14 m high. The elastic gate is 0.005 m thick and 0.079 m high. Before the test starts, there is no deformation of the gate, because the water pressure force and external force provided by a baffle are balanced. When the test starts, the baffle is removed immediately. Under the action of water pressure, the elastic gate deforms and its end moves. Parameters of the simulation can be founded in Table 4.

Fig. 19 presents some snapshots of experiment and their counterparts of the simulation. Some typical phenomena can be captured in both experiment and simulation. Before t = 0.16s, the water level near the elastic gate is lower than that near the right rigid wall. After t = 0.16 s, the water level near the right rigid wall drops faster than that near the elastic gate. In the simulation, the pressure field of the fluid is smooth and obvious non-physical oscillations can not be observed. Besides, the stress field is provided. Tension and compression stress of the structure are in accordance with the actual situation.

Figs. 20 and 21 show the quantitative comparisons between the experiment (Antoci et al., 2007) and simulation. Both the horizontal and vertical displacement of the free end of the gate first increase and then decrease with the drop of water level. The displacement reaches the peak at around t = 0.15 s. The peak of horizontal displacement measured by simulation is slightly higher than experimental results. This discrepancy may arise from the location of left wall. There is no actual left wall in present simulation and the particles will be deleted once they are out of the calculation domain. In general, simulation results match well with experimental data, showing the accuracy of present solver.

3.4. Sloshing flows in a rolling tank with a thin elastic plate

The simulation of periodic motion needs high stability of the solver. The sloshing flows in a rolling rectangular tank with a thin elastic plate fixed in the middle of the bottom is simulated. Fig. 22 shows the sketch of the model. The rectangular tank is 0.609 m wide and 0.3445 m high. The tank is partially filled with oil, which is 0.1148 m deep. The elastic plate is 0.004 m thick and its length is equal to the depth of the oil. Other parameters of simulation can be founded in Table 5. Tank rolls harmonically under the external excitation.

θ= θa sin(ω t) (39)

where A is the amplitude of motion (θa = 4◦), is the excitation frequency (ω = 5.188 rad/s).

Snapshots of moving tank obtained by MPS-DEM and their corre-sponding experimental photos by Idelsohn et al. (2008a) are shown in Fig. 23. The large deformation of the elastic plate can be observed with oil flowing in the tank. When the tank rotates clockwise, the oil on the left-side flows over the plate. The fluid pressure on the left side is obviously higher than that on the right side, making the plate bend to the right. The flow patterns and the bending curve of the plate in the simulation are consistent with those in the experiment. The pressure/-stress fields are both smooth and non-physical oscillations do not occur in the whole simulation.

The time histories of the free end displacement of the elastic plate are presented in Fig. 24, where the numerical results with and without PT technique are compared against the experimental data. It can be noticed that the MPSDEM-SJTU solver with PT performs better than that without PT in terms of phase and peak value. The time histories of pressure measured by probe is presented in the Fig. 25. The peak values of the pressure time histories obtained by the solver with PT obviously larger than that of the solver without PT. The main reason is that the particles on the other side of the plate provide their pressure for the

probe in the simulation without PT, but those particles do not affect the probe in the actual situation. Therefore, it is necessary to use the PT to avoid the interaction between the neighbor particles from different side of the plate. In addition, compared with the pressure measured on the rigid wall of a 2-D sloshing tank in previous work (Xie et al., 2020), the pressure measured on the elastic plate does not oscillate more violently, which also proves that MPSDEM-SJTU solver has the characteristics of better stability.

3.5. Dam-break with an elastic baffle

A sketch of the numerical model corresponding to the dam-break with an elastic baffle in the front of the tank is presented in Fig. 26. The tank is 0.584 m wide. The water column is 0.146 m wide and 0.292 m high, which is placed at the left side of the tank. The elastic baffle is 0.012 m thick and 0.08 m high, which is 0.286 m away from the left wall of the tank. The bottom of the baffle is fixed to the tank while the top is free. Other parameters of the simulation are presented in Table 6.

The snapshots of present numerical results are compared with those simulated by coupling method of MPS and FEM (Mitsume et al., 2014) as shown in Fig. 27. When the dam-break flows impact on the elastic baffle, the obvious deformation occurs in the middle side of the baffle firstly. Then, the free end moves fast to the right under the water pressure. At t = 0.15 s, the water front runs out of the obstacle and an obvious tongue jet can be observed. The displacement reaches the peak at around t =0.2 s. With the drops of water level, the water pressure applied on the baffle decreases, resulting in a smaller deflection. Jet flow further col-lides the right literal wall. Some of fluid climbs up along the wall, while the other moves downward the wall. The deformation of structures and the shape of free surface by present solver are in good agreement with those by (Mitsume et al., 2014). The pressure field is smoother in present simulation.

In addition, the displacement time histories of the free end of the baffle obtained by MPS-DEM are compared with the data of PFEM (Idelsohn et al., 2008b), SPH (Liu et al., 2013) and MPS-FEM (Mitsume et al., 2014) as shown in Fig. 28. Overall, different results follow the same trend. The negative displacement can be observed as the fluid reaches the baffle. Then, the displacement increases sharply and reaches a peak at t = 0.25 s. Due to the water reduction, the displacement de-creases gradually. At t = 0.6 s, the water bouncing back from the wall reaches the right side of the baffle and the displacement abruptly de-creases. It can be seen that numerical oscillations exist in the study by MPS-FEM, which contributes to the non-smooth variation of the displacement from the blue curve. The same phenomenon can also be observed in the results by MPS-DEM at t = 0.2 s.

3.6. Dam-break with a thin elastic plate

The dam-break flows impacting a thin elastic plate has been inves-tigated by Liao et al. (2015) through the experiment and FDM-DEM coupling numerical method. In this sub-section, the case is simulated by MPS-DEM coupling method. Fig. 29 shows the numerical model. The tank is 0.8 m wide. The water column is 0.2 m wide and 0.4 m high, which is placed at the left side of the tank. The elastic plate is 0.004 m thick and 0.09 m high, which is 0.6 m away from the left wall of the tank. The bottom of the plate is fixed to the bottom of the tank while the top is free. Other parameters of the simulation are presented in Table 7.

Fig. 30 shows some typical snapshots of the experiment (Liao et al., 2015) and the simulation. It can be found that the fluid flows along the plate without detachment during the whole impacting process in the experiment while an obvious gap can be observed between the fluid and the plate at t = 0.30 s in the simulation. This unphysical numerical phenomenon is discussed in detail by Sun et al. (2018, 2019c, 2020). Sun et al. (2018) proposed a TIC technique for the SPH method to handle the tensile instability, which can capture the negative pressure near the interface. Due to the existence of negative pressure, the fluid can absorb

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the plate. For the whole stability of the simulation, the conservative scheme is adopted in this paper. The TIC technique will be introduced to MPS-DEM coupling method and the stability will be also considered in the future. The pressure/stress field provided by MPSDEM-SJTU solver has no unphysical gap and the shape of the plate at different instants are well matched with those of experiment.

The time histories of the horizontal displacement of the plate end are presented in Fig. 31. The MPS-DEM results are compared against the FSI- SPH results (Sun et al., 2019b) and experimental data. The overall trend of the results of MPS-DEM with PT is in good agreement with experi-mental data. However, a strong reverse oscillation can be observed during the duration 0.4 < t < 0.7 in both FSI-SPH and MPS-DEM results, which has discrepancy with experimental data. This phenomenon is not observed in the simulation by multi-phase FSI-SPH (Sun et al., 2019b) due to the air cushion effect. Besides, this case is also simulated by MPS-DEM without PT. Its result agrees well with other results when the fluid does not arrive at the right side of the plate (t < 0.4). It can be noticed the reverse oscillation in the simulation of the MPS-DEM without PT is not as strong as that of the MPS-DEM with PT. when t > 0.8, the displacement histories measured by MPS-DEM without PT do not drop as fast as other results. These differences are due to that the particles at different side of the plate are added to the neighbor lists, which reduces the pressure difference on two sides of the plate.

3.7. Fluid-structure interaction with fracture

In the complicated ocean environments, marine structures are prone to failure under the action of extreme load. In this sub-section, the MPSDEM-SJTU solver is extended to the simulation of FSI problems with structural fracture. Fig. 32 presents the sketch of the model. The water is placed at the right side. The top of a thin elastic gate is fixed on the rigid wall while its bottom is free. The water column is 0.089 m wide and 0.18 m high. The thin elastic gate is 0.004 m thick and 0.079 m high. Other parameters of the simulation are presented in Table 8.

Fig. 33 presents simulation snapshots of FSI problem with fracture. The dam-break flows impact the thin elastic gate at t = 0.133 s. The gate deforms and the maximum tensile/compression stress and shear stress can be found near the connection between the gate and rigid wall. The gate broke at t = 0.14 s and the position of the fracture is also around the connection. The fracture-end becomes free and the stress disappears, which corresponds with the actual situation. The broken gate moves forward under the action of flows. Some fluid climbs up the gate and forms a jet flow, which impacts the fracture surface at t = 0.2 s. Therefore, it is necessary to change the type of the boundary particles. The numerical results are reasonable, which shows that MPSDEM-SJTU solver has the potential to tackle the FSI problems with fracture.

4. Conclusions

In this paper, the MPS-DEM coupling method is developed to solve FSI problems. The fluid field is modelled by MPS while the deformations of the structures are simulated by DEM. The particles of the structures have characteristics of MPS and DEM. Information, such as force, ve-locity and displacement, exchanging between MPS and DEM are ach-ieved by interpolation.

In order to enhance the computational efficiency, the parallel tech-nique is introduced to the MPS-DEM method. The misjudgment of neighbor particles near the thin structures can not be ignored in some cases. Therefore, the Partition Technique (PT) is proposed to remove the particles, which are at different sides of the thin structures, from the neighbor list.

The DEM-based structure model is validated firstly by simulating an oscillating cantilever plate. The displacement time histories of the plate with different resolutions match well with the analytic solutions, showing the good convergent performance of DEM solver. Besides, the stress field is continuous and smooth. Then, the MPS-DEM coupling

method is used to solve some FSI problems with deformation, such as the hydrostatic water column on an elastic plate, flood discharge with an elastic gate, sloshing flows in a rolling tank with a thin elastic plate and dam-break with an elastic plate. The parallel efficiency is tested in the hydrostatic case and the running speed of the solver is improved obvi-ously. In the cases with thin structures, the results provided by the solver with PT is more accurate than those by the solver without PT. Finally, the developed solver is successfully extended to tackle the FSI problems with fracture. In general, the developed MPSDEM-SJTU solver can accurately solve the 2-D FSI problem with high performance.

In fact, real ocean engineering problems are more complicated and 3- D effect can not be ignored. However, with the increase of the number of particles, the computational speed will decrease sharply. In the future, 2- D MPS-DEM method will be extended to 3-D. GPU techniques and multi- GPU techniques based on MPI techniques will be introduced to the MPS- DEM method. Besides, the FSI problem with fracture is only roughly simulated by present solver. However, the crack propagation is more complex. The fracture DEM model in present solver should be further improved and validated.

CRediT authorship contribution statement

Fengze Xie: Data curation, Writing – original draft, Visualization, Investigation, Software, Validation. Weiwen Zhao: Software, Data curation, Visualization, Investigation, Validation. Decheng Wan: Su-pervision, Conceptualization, Methodology, Investigation, Writing – review & editing.

Declaration of competing interest

The authors declare the following financial interests/personal re-lationships which may be considered as potential competing interests:

Decheng Wan reports financial support was provided by Shanghai Jiao Tong University.

Acknowledgements

This work is supported by the National Key Research and Develop-ment Program of China (2019YFC0312401 and 2019YFB1704200), National Natural Science Foundation of China (51879159), to which the authors are most grateful.

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