Smoothed Particle Hydrodynamics Method Research Articles

A discontinuous smooth particle hydrodynamics method for modeling deformation and failure processes of fractured rocks

A discontinuous smoothed particle hydrodynamics (DSPH) method considering block contacts is originally developed to model the cracking, frictional slip and large deformation in rock masses, and is verified by theoretical, numerical and/or experimental results. In the DSPH method, cracking is realized by breaking the virtual bonds via a pseudo-spring method based on Mohr–Coulomb failure criteria. The damaged particles are instantaneously replaced by discontinuous particles and the contact bond between the original and discontinuous particles is formed to simulate the frictional slip and separation/contraction between fracture surfaces based on the block contact algorithm. The motion of rock blocks and the contact force of discontinuous particles are determined following Newton's second law. The results indicate that the DSPH method precisely captures the cracking, contact formation and complete failure across six numerical benchmark tests. This single smoothed particle hydrodynamics (SPH) framework could significantly improve computational efficiency and is potentially applicable to broad multi-physical rock engineering problems of different scales.

Fluid–structure interaction modeling of bi-leaflet mechanical heart valves using smoothed particle hydrodynamics

Heart valves are essential for maintaining unidirectional blood flow, and their failure can severely affect cardiac functions. The use of artificial heart valves as replacement has proven to be a reliable and effective solution. Computational fluid dynamics has emerged as a powerful numerical tool for investigating the design, performance, and malfunctioning of mechanical heart valves without the need for invasive procedures. In this study, we employed smoothed particle hydrodynamics (SPH) in an open-source code “DualSPHysics,” to study the hemodynamics of a bi-leaflet mechanical heart valve (BMHV). The proposed SPH method was validated against the traditional finite volume method and experimental data, highlighting its suitability for simulating the heart valve function. The Lagrangian description of motion in SPH is particularly advantageous for fluid–structure interaction (FSI), making it well-suited for accurately modeling the heart valve dynamics. Furthermore, the SPH/FSI technique was applied to investigate the hemodynamic abnormalities associated with BMHV dysfunction. This work represents the first attempt to use SPH to model flow through a realistic BMHV by incorporating FSI. The normal and altered flow behavior and the movement dynamics of the BMHV under various blockage scenarios have also been investigated along with the potential risks of the blocked mechanical valve. The findings demonstrate that this SPH/FSI approach provides a unique, effective, and valuable tool for accurately capturing the transient hemodynamic behavior of bi-leaflet heart valves and its versatility enables the application to more complex patient-specific issues related to cardiovascular diseases.

Three-dimensional numerical study of two drops impacting on a heated solid surface by smoothed particle hydrodynamics

This paper presents a numerical study of a pair of water drops simultaneously and non-simultaneously impacting on a heated surface using smoothed particle hydrodynamics (SPH). The present SPH method is validated qualitatively and quantitively with available experiment results for the impact of single, simultaneous, and non-simultaneous drops on the solid surface. Numerical simulations are performed at the Weber number in the range of 20–117, surface temperature in the range of 25–250 °C, and pressure in the range of 1–20 bar. In the simulations, the coalescence, breakup, and evaporation of the drops are considered. After the collision of the two drops, the hydrodynamic behavior of the uprising sheet height and spreading areas are investigated by considering the horizontal and vertical distances between the two drops, Weber number, surface temperature, and elevated pressure. The numerical results indicate that the Weber number and horizontal distance significantly influence the height of the rising sheet and the spreading area. Conversely, the vertical spacing does not affect the rising sheet height or spreading area. The drop rebound height increases with the wall temperature in the film boiling regime for high boiling point liquids at atmospheric pressure. The effect of ambient pressure on drop rebound height is investigated for simultaneous and non-simultaneous impacts. According to the numerical results, the pressure increase causes a decrease in droplet rebound height.

SPH Simulation of the Interaction between Freak Waves and Bottom-Fixed Structures

In this paper, the Smoothed Particle Hydrodynamics (SPH) method is used in a C# environment to simulate the interaction between freak waves and bottom-fixed structures by establishing a fluid dynamics model. Paraview software 5.10.1 was used to analyze and visualize the simulation results. In order to simulate wave propagation accurately, the reliability of the model was verified by comparing experimental and simulated data. A two-dimensional numerical wave flume was established based on the SPH method, a conservative Riemann solver was introduced, a repulsive boundary condition was adopted, and a slope was used to eliminate wave reflection. Bottom-fixed structures of different heights and lengths, as well as different wave conditions, were selected to numerically simulate the interaction between freak waves and bottom-fixed structures. The results show that the height of bottom-fixed structures and wave conditions have a significant effect on hindering the propagation of rogue waves, while the length has little effect on the propagation of deformed waves. When the amplitude of the wave remains constant, both the period andthe duration of the deformed wave are longer. This research is of certain significance for the prediction of freak waves in marine engineering and the application and promotion of SPH methods.

Implicit Surface Tension for SPH Fluid Simulation

The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force based approach for the simulation of surface tension effects using the Smoothed Particle Hydrodynamics (SPH) method. We define a continuous formulation inspired by the properties of surface tension at the molecular scale which is spatially discretized using SPH. An adapted variant of the linearized backward Euler method is used for time discretization, which we also strongly couple with an implicit viscosity model. Finally, we extend our formulation with adhesion forces for interfaces with rigid objects. Existing SPH approaches for surface tension in computer graphics are mostly based on explicit time integration, thereby lacking in stability for challenging settings. We compare our implicit surface tension method to these approaches and further evaluate our model on a wider variety of complex scenarios, showcasing its efficacy and versatility. Among others, these include but are not limited to simulations of a water crown, a dripping faucet, and a droplet toy.

A dynamic simulation tool for ship's response during damage-generated compartment flooding

Survivability of ships in damaged condition is an issue of paramount importance. Therefore, the regulatory framework is constantly updated, in response to the societal aversion towards accidents with severe impact on human life and on the environment. The introduction of the probabilistic damage stability framework was a major step towards the rationalization of the procedure for the assessment of survivability of ships in damaged condition. Subsequent revisions of SOLAS 2009 included the increase of the safety standard via the new formulations for the R-Index and for the calculation of the probability of survival (s-factor), which however is still performed by a hydrostatic approach. Flooding simulation tools can be used for an in-depth investigation of the transient response of a damaged ship, aiming to identify conditions that could jeopardize her survivability during the initial phases of flooding, or to assist in the improvement of the s-factor formulation. In this work, a newly developed flooding simulation tool, employing the Smoothed Particles Hydrodynamics (SPH) method coupled with a ship motions solver, is presented. The developed methodology predicts the dynamic response of the ship during the flooding process, primarily focusing on the initial stages, when particularly violent flow phenomena may be observed.

Two-phase modelling of erosion and deposition process during overtopping failure of landslide dams using GPU-accelerated ED-SPH

Erosion and deposition induced by overtopping flow strongly impacts the breaching evolution of landslide dams. However, these two processes are not yet sufficiently captured in current dam breaching models. In this paper, we simulate the Erosion and Deposition process during overtopping dam breaching using a novel Smooth Particle Hydrodynamics (ED-SPH) method. A new multi-function boundary is proposed to prevent the penetration of water and soil particles and ensure steady inflows. Dam break and movable erosion scenarios are simulated as a means to validate the model. Dam breach simulations using the ED-SPH method reveal that the proposed model can capture the complex dam soil erosion, entrainment, and depositions behaviors. The soil deposition hinders the eroded particle movement and reduces the water velocity at the water-soil interface. If soil deposition is not considered, as in many existing models, the breaching time decreases and the outburst flood discharge is magnified. We further investigate the re-erosion of deposited soils by varying the re-erosion coefficient. With decreasing the re-erosion coefficient, the peak discharge increases whereas the residual dam height decreases due to the blockage by the deposited soils.

Numerical simulations of Phan-Thien-Tanner viscoelastic fluid flows based on the SPH method

Numerical simulations of viscoelastic fluid flows are always a hot issue in the field of computational fluid dynamics and the study of their complex rheological properties has important academic and engineering application value. In the present work, we develop a smoothed particle hydrodynamics (SPH) method for simulating transient viscoelastic fluid flows governed by the Phan-Thien-Tanner (PTT) constitutive equation. To improve the computational accuracy of the SPH method, the mixed symmetric correction algorithm of kernel gradient is implemented. To remove the particle clustering and unphysical fracture in fluid stretching which is named as the tensile instability, the artificial stress model is added into the momentum equation. We firstly apply the proposed SPH method to solve the plane Poiseuille flow of a PTT viscoelastic fluid, in which the effectiveness and advantage of the method are verified by comparing the SPH solution with those obtained by the finite volume method (FVM) and analyzing the l2 norm error of different SPH solutions to the FVM solution. Then, the method is employed to simulate the impact behavior of a PTT viscoelastic droplet with a rigid plate. In particular, we not only investigate the spreading behavior of PTT viscoelastic droplet after impacting the rigid plate, but also for the first time capture and analyze the bouncing behavior of droplet by decreasing the Reynolds number. The influences of the Reynolds number, the Weissenberg number, the solvent viscosity ratio, and the PTT elongational parameter on the droplet dynamics behavior are further deeply studied. Numerical results demonstrate that the SPH method proposed in this paper is a powerful computation tool for simulating PTT viscoelastic fluid flows and is capable of effectively describing their complex rheological properties and free surface variation characteristics.

Improved MPS models for simulating free surface flows

Two improved Laplacian models are introduced in this study for more accurate simulation of free surface flows in the context of the moving particle semi-implicit (MPS) method, a well-known mesh-less approach. The Euler equations are the governing equations of these flows without considering viscous forces which are solved in the Lagrangian frame by the MPS and two-step projection methods for spatial and temporal discretization, respectively. Considering the similarity between the MPS and SPH (smoothed particle hydrodynamics) methods, one of the introduced Laplacian models is formulated by a corrective matrix firstly proposed in an improved SPH method [28]. The other modified Laplacian model is also derived from the divergence of a newly developed MPS gradient model proposed for solving elasticity problems [33]. The higher accuracy of these methods compared to the classic SPH, MPS and even three modified SPH and MPS Laplacian models [7, 34, 44] is verified by solving 2D Poisson equations. Moreover, the excellent performance of the Laplacian models and the improved gradient model in obtaining smooth pressure field is validated by solving three benchmark free surface flows. Furthermore, the problem of wave damping in the original MPS computations can be resolved by using the applied models.

Numerical study on atmospheric explosive welding based on the 2D structured arbitrary Lagrangian-Eulerian method

Smooth particle hydrodynamics (SPH) is often adopted to simulate the waveform interface, which has a crucial effect on the bonding quality in explosive welding (EXW). However, owing to the nature of the SPH method, it is difficult to evaluate the influence of the air medium and calculate detailed waveform structure. In this study, a Cu-Q235 steel EXW model containing air medium was established using a structured arbitrary Lagrangian-Eulerian (S-ALE) method. A full-size 2D model was first performed to acquire welding parameters, which were set to the initial conditions for the next oblique collision method. Subsequently, the experiment was conducted to verify the accuracy of the simulations. The results show that the S-ALE method can effectively predict the waveform and acquire the detailed process of the EXW. With the addition of an air medium, the calculated velocity and pressure of the shock wavefront were approximately 3300 m·s−1 and 15 MPa, respectively. Despite the limited effect of the gas shockwave on the overall waveform, the influence on the large-scale or thin plates cannot be ignored. Furthermore, the simulation indicates that the participation of the air during the wave formation led to the generation of the pore in the vortex zone. The proposed method could predict the waveform structure and optimize the manufacturing process of composite plates in the atmospheric EXW.

An improved Riemann SPH-Hamiltonian SPH coupled solver for hydroelastic fluid-structure interactions

The paper presents a novel Lagrangian meshfree computational solver for simulation of hydroelastic fluid-elastic structure interaction (FSI) problems. An explicit Smoothed Particle Hydrodynamics (SPH) method, referred to as Riemann SPH, is adopted as the fluid model, and a SPH method within the Hamiltonian framework, namely Hamiltonian SPH (HSPH), is considered as the structure model. A two-way coupling between fluid and structure models is performed in a consistent manner, resulting in a coupled RSPH-HSPH hydroelastic FSI solver. For enhancement of accuracy and robustness of the proposed FSI solver, four refined schemes are incorporated for the fluid and structure models. These four refined schemes include (i) a novel dissipation limiter in the fluid's continuity equation for enforcing the volume conservation, (ii) a refined reconstruction of the quantities in Riemann SPH in the presence of a potential field, (iii) a modified velocity-divergence error mitigation term in the fluid's momentum equation for enhanced satisfaction of the incompressibility condition, and (iv) a Riemann diffusion term in the structural momentum equation for enhanced stability and robustness. Validations of the proposed FSI solver are carried out through a series of fluid, structure and FSI benchmark tests.

Beaching process of floating marine debris associated with the evolution of the nearshore wave

Floating marine debris (FMD) is a pervasive problem in marginal seas worldwide. Driven by the nearshore waves, the FMD gradually accumulates shoreward and has a large chance of being beached, posing a direct threat to the coastal environment. Thus, investigating the nearshore drifting and beaching process of the FMD is of paramount importance. In this article, the trajectories of the FMD on a sloping beach are simulated by the Smoothed Particle Hydrodynamics (SPH) method, which is pre-verified through laboratory experiments. A series of sensitivity tests are conducted numerically on the influence of attributes of FMD as well as varied wave height (H0), and wave period (T0) on its beaching process. It is found that the beaching process of the FMD can be divided into three steps: drifting in front of surf zones, surfing and leaping with plunging waves, and advancing via wave runup. The density of the FMD combined with wave steepness determines whether the FMD can enter into the surf zone where it has a large chance to beach. Finally, this article proposed a semi-analytical model with improved Morison's equations considering the second-order Lagrangian transport on a sloping beach. This semi-analytical model is much faster and is comparable in computational accuracy to the high-resolution SPH model. It has the potential to be incorporated into the existing marine models and replace the stochastic process assumed for the FMD's tracking in the nearshore, in order to achieve more accurate assessment on the stranded FMD.

Simulation of granular surface flows using incompressible non-Newtonian SPH (INNSPH) method

This study presents a comprehensive continuum approach to modeling granular surface flows using the Incompressible Non-Newtonian Smoothed Particle Hydrodynamics (INNSPH) method. The model integrates an incompressible SPH method, where pressure is computed by solving a pressure-Poisson equation with a non-Newtonian rheology. Projection-based SPH has a strong and rigorous theoretical basis can lead to stable and accurate simulations. This paper aims to develop a projection-based SPH method for modeling complex granular flows. INNSPH method combines incompressible SPH and μ(I) rheology models to simulate non-Newtonian viscoplastic fluid behavior in granular flows. Surface deposition, and velocity and pressure fields are estimated using a rheology model. Validation is performed by comparing simulation results, including surface profiles and run-out distances with experimental data, showing good agreement. INNSPH method is then employed to model a 2D column collapse and a dam-break scenario on horizontal and inclined planes for sands and glass beads. The method captures three distinct final deposition morphologies; truncated cone, conic, and Mexican hat shapes in collapsing columns. INNSPH computational efficiency enables simulations of large-scale granular flows, and its open-source nature facilitates collaboration and further modifications by researchers. The method provides a good understanding of granular flow dynamics in various industrial applications including powder technology.

Progressive Dam-Failure Assessment by Smooth Particle Hydrodynamics (SPH) Method

The dam-break water flow is a complex fluid motion, showing strong nonlinearity and stochasticity. In order to better study the characteristics of the dam burst flood, the smooth particle hydrodynamics (SPH) method was chosen to establish a two-dimensional classical dam-burst model, and the flow velocity distribution graph was obtained by calculation and compared with the experimental results in the literature, and the fitting degree of the two was obtained to be 88.4%, which verifies the validity of the model. On this basis, according to the principle of dam failure, the two failure modes of equal-interval gradual failure and progressive gradual failure were simulated, and the water body characteristics such as water flow velocity, energy, pressure, etc., were analyzed based on the different working conditions of the two modes to obtain the characteristics of gradual dam-failure water flow under the two kinds of numerical models. The simulation results show that, compared with the instantaneous dam failure mode, (1) the flow rate of the dam-failure stream reaching the downstream slows down in the gradual dam-failure mode; (2) the depth development of the breach extends downward in layers and stages over time, and the overall duration of the breach is prolonged; (3) the destructive power of the dam-failure flood is weakened as the number of segments increases. The results of the study show that, compared with the instant dam-failure mode, the calculation results of the breach development considering the progressive gradual dam-failure mode are more in line with the theoretical solution and closer to the actual process of dam failure, which can provide ideas and references for advancing the numerical study of dam failure.

Research on the sloshing characteristics of the ship tank with baffles under rolling motion based on smoothed particle hydrodynamics method

The problem of liquid sloshing is widespread in the field of naval architecture and ocean engineering. During the sloshing process, the liquid will produce a large slamming force on the bulkhead. At the same time, the coupled sloshing of the liquid in tank and the hull will also affect the floating state and stability of the hull, and even induce safety accidents. The tank sloshing simultaneous with baffles and under rolling excitation is particularly focused in this paper, which is rarely concerned preciously. Based on the theory of fluid dynamics, the program of tank sloshing under large-amplitude rolling conditions by the smoothed particle hydrodynamics method is compiled, and the accuracy of the numerical model is validated through existing experimental results. Furthermore, the slamming pressure and the wetted height of the tank wall are studied for the cases of different excitation amplitudes and excitation frequencies. Then, the dynamic response characteristics of the sloshing tank with vertical and horizontal baffles are studied, and the effects of different baffle lengths are analyzed. The result shows that under rolling excitation the vertical baffle longer than the water depth can mitigate sloshing to some extent, but the vertical baffle whose length is less than the water depth and the horizontal baffles cannot play a role in mitigating the sloshing.

Numerical Study of Fluid–Solid Interaction in Elastic Sluice Based on SPH Method

In this paper, the fluid–solid interaction problem involving structural movement and deformation is considered, and an SPH (smoothed particle hydrodynamics) interaction method is proposed to establish a numerical fluid–solid model and to correct the particle velocities in the momentum conservation equations. It is found that, when the smoothing coefficient is equal to 0.93, the similarity of the free surface curves reaches up to 91.9%, and calculations are more accurate. Under the same working conditions, the classical model of elastic sluice discharge is established based on the SPH method and the finite element method, and the validity and accuracy of the model based on the SPH method are verified by analyzing the flow pattern of the sluice discharge, the opening of the elastic gate, and the change trend in the free liquid surface curve. On this basis, a number of characteristic points on the sluice gate are selected based on the SPH model to investigate the change rule of pressure at the fluid–solid interface, and the results are as follows: (1) based on the numerical model established by the SPH method, the flow pattern of the water, the opening of the elastic gate, and the change in the free liquid level curve are all in better agreement with the experimental results in the literature than those of the finite element method, and the computational results are also better; (2) the pressure of the solid on the fluid at each characteristic point is equal to the pressure of the fluid on the solid, which satisfies the principle of action–reaction and laterally verifies the nature of the dynamic boundary between the fluid and the solid, further verifying the validity of the program; and (3) in the process of sluice discharge, the elastic sluice presents a large force at both ends and a small force in the middle, meaning that the related research in this paper can act as a reference for flow–solid interaction problems related to sluice discharge.

River-Blocking Risk Analysis of the Bageduzhai Landslide Based on Static–Dynamic Simulation

Landslides blocking rivers in alpine canyon areas can cause great harm. Taking the Bageduzhai landslide on the southeastern margin of the Qinghai-Tibet Plateau as an example, the risk of landslides blocking rivers is analyzed by static analysis and dynamic simulation. Through onsite investigation, it is found that the Bageduzhai landslide is a traction-falling landslide, and there are two sliding surfaces: deep and shallow. Through static analysis of the stability of the Bageduzhai landslide under ordinary rainfall conditions and high-intensity rainfall conditions, the sliding surface position is obtained. On this basis, the smooth particle hydrodynamics method is used to analyze the movement process and accumulation form of the landslide under different working conditions. The analysis results show that the instability volume and sliding surface depth of the landslide under ordinary rainfall conditions are significantly smaller than those under high-intensity rainfall conditions. The instability volume and sliding surface depth under ordinary rainfall conditions can reach 31 m. The river-blocking depth under extreme rainfall conditions can exceed 65 m. The research results provide theoretical support for the risk analysis of the potential river-blocking disaster of the Bageduzhai landslide.

Verification of 3D DDA-SPH coupling method and its application in the analysis of geological disasters

At present, discontinuous deformation analysis (DDA) is in an active development stage and its application in the field of geohazards is expanding. Recently, the DDA method has been coupled with smooth particle hydrodynamics (SPH) to analyze some geohazards involving fluid-solid interactions (FSI) and has shown good prospects in the field. However, the interaction between rocks and water in geological disasters is extremely complex and the comprehensive verifications of the simulation results between the block and fluid under different interactive modes are never found. To solve this problem, we first introduced the basic principle of the DDA and SPH method, followed by the coupling algorithm of the two methods. Then, the correctness of the coupling method was verified through analyses of fluid and solid movement by adopting the dam break test, Scott Russell's wave generator experiment, water entry test of a single sphere, and landslide-generated impulsive wave, which represent different interaction modes between blocks and fluids respectively. Finally, based on the 3D DDA-SPH method, this paper simulated the chain disasters of the water inrush induced by tunnel collapse and the dam instability induced by slope sliding, and analyzed the chain mechanism between the different disasters, which illustrates the feasibility of 3D DDA-SPH coupling method in simulating the FSI problem in geotechnical engineering.

A massive MPI parallel framework of smoothed particle hydrodynamics with optimized memory management for extreme mechanics problems

The dynamic failure process of structures under extreme loadings is very common in many fields of engineering and science. The smoothed particle hydrodynamics (SPH) method offers inherent benefits in dealing with complex interfaces and large material deformations in extreme mechanics problems. However, SPH simulations for 3D engineering applications are time-consuming. To address this issue, we introduce MPI (Message Passing Interface) in our SPH scheme to reduce computational time. Some optimizations are adopted to ensure the massive computation of the SPH method. In particular, an optimized memory management strategy is developed to control the memory footprint. With the present MPI-based massive parallelization of the SPH method, several validation examples are tested and analyzed. By comparing the present numerical results with the reference data, the dynamic failure process of complex structures subjected to extreme loadings like explosive and impact loadings can be well captured. A large number of particles, up to 2.04 billion, are adopted in the present simulations. The scaling tests show that the scalability of the massively parallel SPH program achieves a maximum parallel efficiency of 97% on 10020 CPU cores.

Three-Dimensional Modeling of Tsunami Waves Triggered by Submarine Landslides Based on the Smoothed Particle Hydrodynamics Method

Submarine landslides are a global geohazard that can displace huge volumes of loose submarine sediment, thereby triggering enormous tsunami waves and causing a serious threat to coastal cities. To investigate the generation of submarine landslide tsunamis, a three-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) method is presented in this work. The model is first validated through the simulation of two underwater landslide model tests, and is then applied to simulate the movement of the Baiyun landslide in the South China Sea (SCS). The kinetics features of the submarine landslide, including the sliding velocity and runout distance, are obtained from the SPH simulation. The tsunami waves generated by the Baiyun landslide are predicted. In addition, sensitivity analyses are conducted to investigate the impact of landslide volume and water depth on the amplitude of the tsunami waves. The results indicate that the amplitude of tsunami waves triggered by submarine landslides increases with the landslide volume and decreases with the water depth of the landslide.