Smoothed Particle Hydrodynamics Method Research Articles

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.

Boundary Treatment with Additive Boundary Particles for Incompressible Smoothed Particle Hydrodynamics Method

A new boundary treatment considering uniform particle distribution using additive boundary particles for the incompressible smoothed particle hydrodynamics (ISPH) method is proposed. With this new boundary treatment, the solid boundary can be easily modeled just following the geometry configuration and consequently the simulations of fluid–structure interaction problems can be simplified. The efficiency of this new boundary treatment is analyzed, and the implementations are compared with other exiting boundary treatments such as repulsive force and ghost particles. Simulations of the 2D dam-breaking case, static tank, and 2D u-tube test are carried out as examples to demonstrate the performance of this new boundary treatment. It is shown that better predictions can be gained with the new boundary treatment for the pressure distribution in these cases than those obtained from other boundary treatments.

Dynamics of a droplet in shear flow by smoothed particle hydrodynamics

The behavior of a droplet under shear flow in a confined channel is studied numerically using a multi-phase smoothed particle hydrodynamics (SPH) method. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet and the matrix fluid, we are able to investigate systematically the droplet dynamics such as deformation and breakup. We conduct the majority of the simulations in two dimensions due to economical computations, while perform a few representative simulations in three dimensions to corroborate the former. Comparison between current results and those in literature indicates that the SPH method adopted has an excellent accuracy and is capable of simulating scenarios with large density or/and viscosity ratios. We generate slices of phase diagram in five dimensions, scopes of which are unprecedented. Based on the phase diagram, critical capillary numbers can be identified on the boundary of different states. As a realistic application, we perform simulations with actual parameters of water droplet in air flow to predict the critical conditions of breakup, which is crucial in the context of atomization.

Investigation of dynamic contact between cold spray particles and substrate based on 2D SPH method

In cold spray, the study of the dynamic contact between the particle and the substrate in the high-velocity impact is essential during particle deposition. To entirely reveals the dynamic contact process, the SPH (Smoothed Particle Hydrodynamics) method is applied to virtual experiments to avoid the time-consuming and high costs in real experiments due to scale. In particular, an interface force model is proposed to completely describe the dynamic contact between the cold spray particles (CS particles) and substrate, which has the ability to eliminate the unphysical SPH particle penetration, rebounding phenomenon, and insufficient momentum transfer. The variation of the steady mean temperature of the CS particle surface with the initial velocity is analyzed and the critical velocity of particle deposition is successfully predicted. Furthermore, the effect of particle shapes on the deposition is discussed, which shows that the circular particles are more favourable to be deposited than the elliptical ones. The cold spray SPH model with the novel dynamic contact developed in this paper is in favor of understanding the mechanism of CS particles deposition and guiding the cold spray processes in a certain extent.

Predicting the Flow Behavior and Residence Time Distribution in Chemical Reactors: A Simplified and Fast Approach Using Smoothed Particle Hydrodynamics

AbstractUnderstanding the flow dynamics of chemical species is important for characterizing, analyzing, and designing chemical reactors. Computational fluid dynamics (CFD) provides accurate flow patterns, but this approach can be computationally expensive for large or complex geometries. To overcome this limitation, a new Lagrangian‐based method is developed using smoothed particle hydrodynamics (SPH) to forecast the flow patterns and residence time distribution of two different fluids for various reactor geometries: (laminar, fractal, T‐mixer, Hartridge–Roughton (H‐R) mixer and packed bed with a gyroid internal packing) and compared the results with computational fluid dynamics (CFD) simulations. The SPH method is less accurate than the CFD analysis, but it obtained the approximate flow behavior much faster. Consequently, the SPH method has significant potential as a first screening technique to optimize reactor topologies and internal packing structures.

An accurate and efficient HOS-meshfree CFD coupling method for simulating strong nonlinear wave–body interactions

The study on strong nonlinear wave–structure interaction (WSI) is crucial in ocean engineering. The Smoothed Particle Hydrodynamics (SPH) method is popular in this field because of its advantages in simulating free surface flow. However, to predict the details of WSI, a high resolution of particles is usually required, which results in a huge computational cost. In this paper, a potential-meshfree CFD weak coupling method based on the High Order Spectral (HOS) and SPH method is developed, which combines the advantages of the former in generating nonlinear waves quickly and accurately and the latter in adapting to strong nonlinear free surface problems. The accuracy of the coupling method was verified through the simulations of regular and irregular waves compared with experiment data. It shows the coupling method can effectively improve computational efficiency and extensively reduce the numerical dissipation. Furthermore, a simulation of the interaction between the focus wave and the floating body was conducted by using the coupling method, the original SPH method and the Constrained Interpolation Profile (CIP) method. Among all numerical methods, the coupling method is the best one for predicting the impact pressure of the floating body and is the only one that can capture the second impacting peak.

Dynamic Temperature Characteristics of Cathode Microprotrusion Under Electron Emission Based on Smoothed Particle Hydrodynamics

The study of dynamic temperature characteristics of cathode micro-protrusion under electron emission would be essential to the development of high-voltage vacuum systems. Owing to the multi-scale and multi-physics characteristics of the micro-protrusions under the electron emission, Smoothed Particle Hydrodynamics (SPH) method has become one of the feasible methods. In this paper, the SPH method is introduced to study the dynamic temperature characteristics of a micron scale micro-protrusion under the electron emission. First, the constitutive model and the equation of state with the material strength, and the coupling effect of the heat conduction, Joule heating, Nottingham effect and electron emission have been introduced into the SPH method. Then, a SPH model of the micro-protrusion under the electron emission with considering the temperature correction is established by combining the SPH method and thermal-field emission heating model. Compared with the Finite Element Method (FEM) and theoretical calculation, the SPH model of the micro-protrusion under the electron emission is verified. Based on the SPH model of the micro-protrusion, the dynamic temperature characteristics under the different conditions are quantitatively obtained and analyzed. The results of this paper may provide some useful reference for the vacuum insulation design and the insulation state evaluation of the high-voltage vacuum system.

Establishment and validation of a viscous-potential coupled and graphics processing unit accelerated numerical tank based on smoothed particle hydrodynamics and high-order spectral methods

The smoothed particle hydrodynamics (SPH) method is an entirely Lagrangian and truly meshless numerical tool that is inherently suitable for simulating violent viscous free-surface flows, whilst it usually renders considerable simulation time when solving large-scale engineering problems. The high-order spectral (HOS) method is an accurate and very efficient numerical tool for modeling a large-scale inviscid gravity wave field, whilst it is hard to tackle complex physical phenomena due to the dependence on the potential flow theory. This paper aims to propose a viscous-potential coupled and graphics processing unit accelerated numerical model for establishing a high-fidelity and high-efficiency numerical wave tank. In this coupling scheme, the SPH method is applied in the near-field where violent physical processes exist to accurately capture complex free-surface behaviors such as overturning and breaking, whilst the HOS method is applied in the far-field where the water undergoes gentle motion to efficiently generate a desired gravity wave. A dedicated SPH–HOS coupling interface is also presented to accurately transmit the flow information from the HOS side to the SPH side. Meanwhile, an SPH–HOS buffer region with several key techniques is also proposed to ensure a successful coupling between the two numerical methods. Different benchmarks demonstrate that the present SPH–HOS coupling method absorbs the respective advantages of the two numerical methods and shows great feasibility and reliability in solving hydrodynamic problems involving gravity wave generation, propagation, deformation, and its interaction with marine structures.

Numerical modeling and simulation of underwater explosions interacting with discrete rigid bodies

The smoothed particle hydrodynamics (SPH) method is widely used to simulate underwater explosion phenomena. However, previous studies have focused on the interaction between the underwater explosion and continuous structures (e.g., steel plates and dams), while studies on the interaction between the explosion and discrete objects (e.g., debris) have not been reported. In this study, a multi-media coupled model containing water, explosion gas, discrete objects, and steel plates is developed based on the SPH method. The discrete object is modeled as a rigid body with a certain shape, which is discretized by SPH particles. The interaction between the discrete object and the adjacent fluid particles is realized by the kernel approximation, while the collision between different objects is realized by the contact algorithm. To improve the numerical stability, an artificial viscous term containing a threshold switch is added to the SPH momentum equation, while a density dissipation term is introduced into the continuity equation to reduce the noise of the pressure field. Subsequently, the established SPH model is used to simulate the underwater explosion process containing discrete rigid bodies, and the effects of the distribution, stacking form, and number of rigid bodies on the propagation of shock waves, bubble expansion, and deformation of steel plates and the effect of damage are analyzed. The results show that the rigid body will hinder the propagation of shock waves, help reduce the peak pressure of the shock wave behind, and then affect the direction of the diffusion of the explosion energy. Shock waves would produce diffraction, reflection, and transmission when passing through the rigid bodies, and the superposition of various waves would make the pressure distribution near the liquid–gas interface irregular. The rigid bodies stacked above the explosives would enhance the damage effect of the explosion on the steel plates below, and the damage effect is affected by the stacking form. The established model can simulate the multi-medium coupling process in a unified framework without coupling other methods and can effectively restore the complex interaction process between underwater explosion, discrete object, and structure.

Exploring the link between coffee matrix microstructure and flow properties using combined X-ray microtomography and smoothed particle hydrodynamics simulations

Coffee extraction involves many complex physical and transport processes extremely difficult to model. Among the many factors that will affect the final quality of coffee, the microstructure of the coffee matrix is one of the most critical ones. In this article, we use X-ray micro-computed (microCT) technique to capture the microscopic details of coffee matrices at particle-level and perform fluid dynamics simulation based on the smoothed particle hydrodynamics method (SPH) with the 3D reconstructured data. Information like flow permeability and tortuosity of the matrices can be therefore obtained from our simulation. We found that inertial effects can be quite significant at the normal pressure gradient conditions typical for espresso brewing, and can provide an explanation for the inconsistency of permeability measurements seen in the literature. Several types of coffee powder are further examined, revealing their distinct microscopic details and resulting flow features. By comparing the microCT images of pre- and post-extraction coffee matrices, it is found that a decreasing porosity profile (from the bottom-outlet to the top-inlet) always develops after extraction. This counterintuitive phenomenon can be explained using a pressure-dependent erosion model proposed in our prior work. Our results reveal not only some important hydrodynamic mechanisms of coffee extraction, but also show that microCT scan can provide useful microscopic details for coffee extraction modelling. MicroCT scan establishes the basis for a data-driven numerical framework to explore the link between coffee powder microstructure and extraction dynamics, which is the prerequisite to study the time evolution of both volatile and non-volatile organic compounds and then the flavour profile of coffee brews.

Research on the Water Entry of the Fuselage Cylindrical Structure Based on the Improved SPH Model

During aircraft landing on water, the intense impact load may lead to significant local deformation of the fuselage skin. Ensuring the aircraft’s integrity and reliability is of paramount importance. This paper investigates the fuselage skin’s dynamic response during water entry. In the simulation of complex water entry problems, the smoothed particle hydrodynamics (SPH) method can fully leverage the advantages of the particle method. However, the traditional SPH method still suffers from the drawbacks of tensile instability, significantly affecting the computational accuracy. Therefore, this paper first introduces the improved SPH model addressing fluid and solid tensile instability issues. Furthermore, the Riemann-based contact algorithm at the fluid–solid interface is also demonstrated. Based on the above improved SPH model, the simulation of water entry of the elastic cylinder is performed to validate the efficacy of the improved SPH model. Then, the dynamic response characteristics of elastic fuselage skin and the skin–stringer–floor–column structure when it enters the water are analyzed, including the deformation features and slamming force. Lastly, based on the presented damage model, a study is conducted on the water entry of the metallic elastic–plastic skin–stringer–floor–column structure, analyzing the locations of failure and providing guidance for the structural safety design of engineering.

A revisit of disaster process of Vajont rockslide using a coupled discontinuous smooth particle hydrodynamics (CDSPH) method

A revisit of disaster process of Vajont rockslide using a coupled discontinuous smooth particle hydrodynamics (CDSPH) method

Simulation of Mouldboard Plough Soil Cutting Based on Smooth Particle Hydrodynamics Method and FEM–SPH Coupling Method

In the field of agricultural machinery, various empirical field tests are performed to measure the tillage force for precision tillage. However, the field test performance is costly and time-consuming, and there are many constraints on weather and field soil conditions; the utilization of simulation studies is required to overcome these shortcomings. As a result, the SPH method and the coupled FEM-SPH method are used in this paper to investigate the mouldboard plough–soil interaction. In this paper, the finite element software LS-DYNA was used to build the SPH model and the FEM-SPH coupling model of soil cutting, as well as to investigate the change in cutting resistance during the soil cutting process. The simulation results are compared with those of the experiments, and the curves of the simulation and experiment are in good agreement, which verifies the reliability of the model. The validated simulation model was used to investigate the effects of the cutting speed, depth of cut, inclination angle, and lifting angle of the mouldboard plough on cutting resistance. The simulation studies show that the SPH model takes 5 h and 2 min to compute, while the FEM-SPH coupled model takes 38 min; obviously, the computational efficiency of the FEM-SPH coupled model is higher. The relative errors between the SPH model and the experiment are 2.17% and 3.65%, respectively. The relative errors between the FEM-SPH coupled model and the experiment are 5.96% and 10.67%, respectively. Obviously, the SPH model has a higher computational accuracy. The average cutting resistances predicted by the SPH model and the FEM-SPH coupled model, respectively, were 349.48 N and 306.25 N; these resistances are useful for precision tillage. The cutting resistance increases with the increase in cutting speed and is quadratic; the cutting resistance increases with the increase in cutting depth and is quadratic; the horizontal cutting resistance and the combined cutting resistance increase with the increase in inclination angle, while the vertical cutting resistance remains essentially constant with the increase in inclination angle; the horizontal cutting resistance and combined cutting resistance increase as the lifting angle increases, while the vertical cutting resistance decreases as the lifting angle increases.

A hybrid Finite Volume-Smoothed Particle Hydrodynamics approach for shock capturing applications

A hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach for shock capturing in compressible fluids is presented. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. New FVM-SPH coupling approaches are explored, including online SPH particle injection and deletion around time persistent SPH regions around shocks. The SPH simulation is coupled to the FVM simulation through boundary particles surrounding the active SPH regions, with FVM values interpolated to SPH boundary particles at each timestep. Values in active SPH regions are similarly interpolated to the overlying FVM mesh at each timestep. The performance of the hybrid FVM-SPH scheme in comparison to the individual FVM and SPH methods on two-dimensional test problems is assessed. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy, although it remains slower than the FVM. This hybrid SPH algorithm may enable future compressible fluid simulations with more extensive capabilities than grid-based methods alone, offering potential applications in modeling fluid–structure interaction and solid deformation and fracturing in blast simulations. Further research will focus on applying the hybrid method to three-dimensional blast problems, where the relative computational cost reduction is expected to be more significant.

Seepage Evolution Law and Deformation Failure Characteristics of Porous Media Based on Smoothed Particle Hydrodynamics

It is difficult to characterize the whole process of seepage movement by traditional numerical methods, which leads to the unclear mechanism of stress-strain change in soil. Therefore, the meshless method smooth particle hydrodynamics method is proposed to study the seepage law and deformation characteristics of soil. Combined with the strain softening model, a nonlinear cohesive force change model of porous media is proposed to accurately describe the evolution characteristics of soil seepage failure. Secondly, the damping coefficient and stress normalization method are used to better eliminate the defects of numerical stress noise generated by soil deformation after boundary interpolation, and improve the accuracy of SPH method in studying the internal stress of soil deformation. It is concluded that the influence of the viscosity coefficient on the unsteady head is significantly higher than that of the constant head. At the same time, the evolution characteristics of soil seepage instability under linear cohesion change are compared and analyzed. It can be seen that the proposed nonlinear cohesion change model is more in line with the actual failure mode of soil seepage. The research results can provide a new method and idea for the study of slope seepage motion range and stability analysis.

Efficient implementation of low-order-precision smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) method is widely accepted as a flexible numerical treatment for surface boundaries and interactions. High-resolution simulations of hydrodynamic events require high-performance computing (HPC). There is a need for an SPH code that runs efficiently on modern supercomputers involving accelerators such as NVIDIA or AMD graphics processing units. In this work, we applied half-precision, which is widely used in artificial intelligence, to the SPH method. However, improving HPC performance at such low-order precisions is a challenge. An as-is implementation with half-precision will have lower computational cost than that of float/double precision simulations, but also worsens the simulation accuracy. We propose a scaling and shifting method that maintains the simulation accuracy near the level of float/double precision. By examining the impact of half-precision on the simulation accuracy and time-to-solution, we demonstrated that the use of half-precision can improve the computational performance of SPH simulations for scientific purposes without sacrificing the accuracy. In addition, we demonstrated that the efficiency of half-precision depends on the architecture used.

Smoothed Particle Hydrodynamics Approach for Simulation of Non-Newtonian Flow of Feedstocks Used in Powder Injection Molding

The present work aims to explore the ability to simulate flow patterns and the velocity field in the powder injection molding (PIM) process using the smoothed particle hydrodynamics (SPH) method. Numerical simulations were performed using the DualSPHysics platform. A feedstock formulated from 17-4 PH stainless steel powder (60 vol. % of powder) and a wax-based binder system was prepared to experimentally obtain its rheological properties that were implemented in DualSPHysics using two different viscosity models. The numerical simulations were calibrated, and then validated with real-scale injections using a laboratory injection press. During the calibration step, the feedstock flow momentum equation in the DualSPHysics code was modified and boundary friction coefficients at different injection rates were adjusted to create a frictional effect. During the validation step, these calibrated conditions were used to simulate the flow behavior into a more complex shape, which was compared with experimental measurements. Using an appropriate boundary friction factor, both the frictional effect of the boundaries and the stability of the numerical solution were taken into account to successfully demonstrate the ability of this meshless SPH method. The flow front length and feedstock velocity obtained in a complex cavity were satisfactorily predicted with relative differences of less than 15%.

A Numerical Study on the Ballistic Performance of Projectiles Formed by Shaped Charge

Abstract In this work, a numerical analysis of shaped charge impact process is conducted to investigate the jet formation process and its penetration performance on metal targets. Numerical results are compared with experimental data from published literature for liners made up of copper and iron. Conical and bowl-shaped liner geometries are simulated with various configurations to observe their effects on projectile shape and penetration capability using the finite element (FE) method. The exact shape of the explosively formed projectile at the onset of impact is modeled as a rigid 3D body to simulate the penetration process. #45 and Armox 500T steels are used as the target materials, and the material behavior and failure mechanisms are modeled using the Johnson–Cook (JC) plasticity and damage models. In addition to the FE method, smoothed particle hydrodynamics (SPH) is utilized as well to evaluate its capacity in predicting the failure behavior of the metal targets. It is concluded that the FE method outperforms the SPH method at predicting failure modes, while SPH can still be used to predict residual velocity and hole diameters. Armox 500T demonstrates a higher impact resistance compared to #45 steel. Liner geometry is found to significantly affect penetration performance. Sharper and thinner projectiles formed from liners with small cone angles are shown to be highly efficient in penetrating through armor steel targets.