Smoothed Particle Hydrodynamics Algorithm Research Articles

Improved mesh-free SPH approach for loose top coal caving modeling

This study presents an innovative model in computational geotechnical engineering by improving the Smoothed Particle Hydrodynamics (SPH) method for simulating loose particle dynamics in coal caving processes. The improved model integrates an elastic-perfectly plastic constitutive model with the Drucker-Prager yield criterion and includes several improvements aimed at boosting accuracy, stability, and efficiency. These improvements include gravity loading coupled with particle damping, first-order stress field smoothing, and kernel gradient correction. A series of numerical experiments validates the effectiveness of the improved SPH model, demonstrating its capability to predict large deformations and track the evolution of the coal-rock interface in coal caving processes. Furthermore, the study analyzes the model's sensitivity to material parameters such as the angle of friction and material density, which aids in configuring the model for distinct coal mining situations. Results show that the non-cohesive elastic-perfectly plastic constitutive model can effectively simulate the flow behavior of granular particles, and the landslide simulation results are in good agreement with the experiments. The improved SPH algorithm with stress smoothing technique solves the problem of numerical noise, and the “double peak” stress distribution around the coal outlet is identified. The established SPH model offers an effective tool for understanding dynamics behaviors of loose top coal. Significantly, the model requires only five material parameters, which can be identified through standard experiments, avoiding the typically arduous process of parameter selection or calibration commonly existing in Discrete Element Method simulations.

Study on Water Entry of a 3D Torpedo Based on the Improved Smoothed Particle Hydrodynamics Method

The water entry of a torpedo is a complex nonlinear problem, involving transient impact, free surface deformation, droplet splashing, and fluid–structure coupling, which poses severe challenges to traditional mesh methods. The meshless smoothed particle hydrodynamics (SPH) method shows unique advantages in capturing the complex features of the water entry of the torpedo at different entry angles. However, it still suffers from some inherent shortcomings, such as low surface discretization accuracy, poor discretization flexibility, and low calculation efficiency. In this study, an improved adaptive SPH algorithm is proposed to investigate the water entry of the torpedo accurately and efficiently. This method integrates meshless point generation and adaptive techniques simultaneously. The numerical results demonstrate that when the torpedo vertically enters the water at different velocities, the induced impact loads acting on the head of the torpedo fluctuate significantly with two peak values in the initial stage and thereafter stabilize in a later stage. The impact load acting on the torpedo, the entry depth of the torpedo, the splash height of the droplets, and the size of the cavity generated around the torpedo increase with the increment in the entry velocity. When the torpedo enters the water at different entry angles under the same initial entry velocity, both the vertical and the horizontal movements of the torpedo are observed, which results in more complex variations in parameters along the x- and y-axes. The findings and the corresponding numerical method in this study can provide a certain basis for the future designs of the entry trajectory and the structural bearing capacity of torpedoes.

Reliability analysis using Limit equilibrium and Smoothed Particle Hydrodynamics-based method for homogeneous soil slopes.

This paper develops a combined method to predict the volume of sliding mass for homogeneous slopes in an efficient manner. Firstly, the failure surface with minimum factor of safety (FS) in Limit Equilibrium Method is equated to that one determined by Smoothed Particle Hydrodynamics algorithm to obtain the threshold displacement value for unstable and stable particles. Secondly, the threshold displacement value is used to identify the volume of sliding mass using SPH. Finally, a regression model is developed based on a finite number of SPH simulations for homogeneous soil slopes. The proposed LEM-SPH based method is illustrated through a cohesive soil slope. It is concluded that the use of failure surface with minimum FS in LEM tends to underestimate the volume of sliding mass and to give an unconservative risk value. The Coefficient of Variation (Cov) of volume of sliding mass are 0.14, 0.28, 0.4, 0.48, 0.53 for Cov of soil properties = 0.2, 0.3, 0.4, 0.5, and 0.6, respectively. The uncertainty of soil properties has a significant effect on the mean value of volume of sliding mass and therefore the landslide risk value. The proposed method is necessitated for cases where large uncertainties in soil properties exist.

Investigations on geopolymer-based seawater sea-sand high performance concrete slabs reinforced with basalt FRP bars under direct contact explosions

Adopting locally available raw materials like seawater and sea-sand in coastal areas and oceanic islands has facilitated meeting the demands of marine engineering. However, these raw materials contain corrosive elements that could threaten the steel reinforcement in concrete structures, thus non-corrosive fibre-reinforced polymer (FRP) bars are proposed. In the present study, the geopolymer-based seawater sea-sand high performance concrete (G-SHPC) slab reinforced with basalt FRP bars was designed to preliminarily evaluate its dynamic behaviour under contact explosions. Tests were conducted on three large-sized slabs with different TNT charge weights, including 0.8 kg, 1.6 kg and 2.2 kg. To complement the experimental investigation, a numerical simulation was then performed in ANSYS-DYNA. A Continuous Surface Cap (CSC) model was developed to accommodate the unique characteristics of G-SHPC. Two different blast modelling methods, including the Arbitrary Lagrangian-Eulerian (ALE) algorithm and a hybrid Finite-Element (FE) and Smooth Particle Hydrodynamics (SPH) algorithm, were examined to faithfully reproduce the contact explosion phenomena. The structural models considered the bond-slip behaviour, and three bond-slip models were compared. The numerical results obtained through the ALE algorithm and the beam-in-solid bond-slip model exhibited fair agreement with the test results, with a maximum error of less than 6.3%. A parametric study was further conducted to establish the damage identification diagram. Formulas based on empirical data were formulated to anticipate the damage degrees of G-SHPC slabs exposed to contact explosions.

Multiscale Smoothed Particle Hydrodynamics based on a domain-decomposition strategy

A multi-resolution algorithm for weakly-compressible Smoothed Particle Hydrodynamics is hereby proposed. The approach chosen is based on a domain decomposition to subdivide the computational domain into regions with different resolutions. Each sub-problem is closed by appropriate Dirichlet boundary conditions that are enforced via buffer regions, populated by particles whose physical quantities are obtained by means of an interpolation over adjacent sub-domains.The algorithm has been implemented into the DualSPHysics open-source code and it has been tested and validated through a series of different study cases. The capability of the numerical scheme to simulate multiscale fluid flow has been demonstrated by solving the flow past a cylinder for a Reynolds number of 9,500 and a ratio between the largest and smallest particle size equal to 28. Furthermore, the proposed SPH multi-resolution algorithm can also be used for flow around moving objects, such as an oscillating cylinder in cross-flow, and free-surface flow, such as the simulation of a triangular wedge impacting on the free surface of a quiescent liquid.

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.

Simulating hyperelastic materials with anisotropic stiffness models in a particle-based framework

We present a particle-based smoothed particle hydrodynamics (SPH) framework for simulating hyperelastic materials with anisotropic stiffness models. While most elastic simulations predominantly rely on mesh-based approaches, such as the Finite Element method, the relationship between Lamé’s first parameter and Poisson’s ratio complicates the strict enforcement of volume conservation, making it challenging to stabilize simulations for common biological tissues like fat and muscle. In this paper, we couple an implicit divergence-free SPH solver with particle-based deformation gradient computation and apply various elastic energy functions to achieve incompressible elastic simulations. The incompressibility of elastic objects and collisions between different bodies are managed by the implicit SPH algorithm. We further incorporate anisotropic energy functions, constructed from the extrapolation of Cauchy–Green invariants, to introduce anisotropic properties to the objects. By integrating activation and contraction coefficients into the energy functions, particles can simulate muscle contractions and lift heavy objects. Our method can effectively represent elastic objects with varying mechanical properties across different directions and be further employed to mimic muscle contractions. Experiments demonstrate that our approach provides realistic simulations for a wide range of animal and human body movements.

Numerical simulations for largely deformed beams and rings adopting a nontensile smoothed particle hydrodynamics algorithm

Three typical elastic problems, including beam bending, truss extension and compression, and two-rings collision are simulated with smoothed particle hydrodynamics (SPH) using Lagrangian and Eulerian algorithms. A contact-force model for elastic collisions and equation of state for pressure arising in colliding elastic bodies are also analytically derived. Numerical validations, on using the corresponding theoretical models, are carried out for the beam bending, truss extension and compression simulations. Numerical instabilities caused by largely deformed particle configurations in finite/large elastic deformations are analysed. The numerical experiments show that the algorithms handle small deformations well, but only the Lagrangian algorithm can handle large elastic deformations. The numerical results obtained from the Lagrangian algorithm also show a good agreement with the theoretical values. doi: 10.1017/S1446181123000160

Quantum algorithm for smoothed particle hydrodynamics

We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a one-dimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a one-dimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gate-based quantum computers.

Using an improved SPH algorithm to simulate thermo-hydro-mechanical-damage coupling problems in rock masses

The Thermo-Hydro-Mechanical-Damage (THMD) process inside rock structures is a complex multi-field coupling problem, which is also regarded as the hotspot worldwide. In view of this situation, a fracture mark ξ is introduced to reflect the “active” or “failure” mode of Smoothed Particle Hydrodynamics (SPH) particles, which can simulate rock progressive cracking characteristics. The solid-water interaction modes and the damaged particles - water particles transformation algorithms are embedded into traditional SPH program to simulate the water-stress coupling problems. The heat conduction equations are programmed into SPH, which can reach the goal of modeling the temperature-stress coupling problems. Results show that: By coupling the parameter transformations between water and solid particles, the thermo-hydro-mechanical-damage simulation is then realized. Three numerical examples are carried out to validate the improved THMD method. Finally, an engineering numerical model of a typical tunnel is established, and the THMD coupling processes under complex conditions are simulated, which shows that the improved SPH method can simulate rock THMD multi-field coupling problems. The research results will help understanding the rock THMD coupling mechanisms, meanwhile, it can also promote the applications of SPH method into THMD modeling.

Simulation of collapse failure process of rock slope based on the smoothed particle hydrodynamics method

The limit equilibrium method (LEM) or finite element method (FEM) for slope problems most frequently focusses on the stability analysis. There are, however, still some problems with the LEM or FEM when considering damage and failure evolution of a rock slope because of the distortion of mesh. In this work, a mesh-free particle approach, named the smoothed particle hydrodynamics (SPH) method, is presented and is improved to analyze the damage and failure process of a rock slope. In order to better describe the cause and mechanism of brittle failure for a rock slope, the plastic factor was suggested and introduced into the SPH algorithm, and the conservation equations of SPH for brittleness characteristics were obtained. Based on the variation of displacement and time, an effective criterion was proposed to define the factor of safety in SPH simulation. The Drucker-Prager Mohr-Coulomb strength criterion was implemented into the SPH algorithm to describe the elastic-plastic behavior. Then, three rock-slope models with different precast cracks were analyzed to illustrate the performance of the proposed method. It is shown that the proposed SPH algorithm can be effectively applied in the prediction of the deformation and failure process of rock slope.

Comparing methods for permeability computation of porous materials and their limitations

AbstractEfficient numerical simulations of fluid flow on the pore scale allow for the numerical estimation of effective material properties of porous media, e.g. intrinsic permeability or tortuosity. These parameters are essential for various applications where hydro‐mechanical properties on larger scales have to be known. Numerical tools based intrinsically on pore scale simulations are known e.g. as Digital Rock Physics in geosciences and have even more and more replaced physical experiments. For these reasons, the validation of numerical methods as well as the establishment of clear limits regarding the application areas play an important role. Here, we compute single‐phase flow through a porous matrix, e.g. irregular sphere packings, sandstones, artificially created thin porous media, on the pore scale. Therefore we implement on the one hand a Smoothed Particle Hydrodynamics algorithm for solving the Navier‐Stokes equations and on the other hand a Finite Difference solver for the Stokes equations. Both methods work directly and seamlessly on voxel data of porous materials which are generated by µXRCT‐scans or by microfluidic experiments that have undergone segmentation and binarization. We compare both solvers from a parallel performance point of view as well as their results for flows in the Darcy regime. In addition, we investigate the limitations of the solvers using the example of a porous material whose pore geometry changes over time and precipitation affects the flow conditions.

An entropy-stable updated reference Lagrangian smoothed particle hydrodynamics algorithm for thermo-elasticity and thermo-visco-plasticity

This paper introduces a novel upwind Updated Reference Lagrangian Smoothed Particle Hydrodynamics (SPH) algorithm for the numerical simulation of large strain thermo-elasticity and thermo-visco-plasticity. The deformation process is described via a system of first-order hyperbolic conservation laws expressed in referential description, chosen to be an intermediate configuration of the deformation. The linear momentum, the three incremental geometric strains measures (between referential and spatial domains), and the entropy density of the system are treated as conservation variables of this mixed coupled approach, thus extending the previous work of the authors in the context of isothermal elasticity and elasto-plasticity. To guarantee stability from the SPH discretisation standpoint, appropriate entropy-stable upwinding stabilisation is suitably designed and presented. This is demonstrated via the use of the Ballistic free energy of the coupled system (also known as Lyapunov function), to ensure the satisfaction of numerical entropy production. An extensive set of numerical examples is examined in order to assess the applicability and performance of the algorithm. It is shown that the overall algorithm eliminates the appearance of spurious modes (such as hour-glassing and non-physical pressure fluctuations) in the solution, typical limitations observed in the classical Updated Lagrangian SPH framework.

Research on non-cohesive jet formed by Zr-based amorphous alloys

The shaped charge jet formation of a Zr-based amorphous alloy and the applicability of different numerical algorithms to describe the jet formed were experimentally and numerically investigated. X-ray experiments were performed to study jet characteristics. The numerical results for the Zr-based amorphous alloy jet formed via the Euler and smooth particle hydrodynamics (SPH) algorithms were compared and analyzed using the Autodyn hydrocode. Particle motion was examined based on material properties. The Zr-based amorphous alloy formed a noncohesive jet driven by an 8701 explosive. Both the Euler and SPH algorithms achieved high accuracy for the determination of jet velocity. When the improved Johnson-Holmquist constitutive model (JH-2) was used, numerical results confirmed the model’s suitability for the Zr-based amorphous alloy. The Euler algorithm effectively reflected jet shape within a short computing time, whereas the SPH algorithm was highly suitable for showing the shape of the jet tail within a long computing time. In the 3D Euler model, the flared jet mouth indicated radial particle dispersion; however, in the 2D model, particle dispersion in the head was directly observed by using the JH-2 material model. The brittle fracture of the material reduced the proportion of particles near the liner apex forming a jet. Furthermore, a new method in which stagnation pressure was used to predict jet formation and its coherence was proposed since the collapse angle was difficult to obtain.

An improved multiphase SPH algorithm with kernel gradient correction for modelling fuel–coolant interaction

Fuel–coolant interaction (FCI) has a pivotal role in the development of core disruptive accident in a sodium-cooled fast reactor. The drastic deformation of multiphase interface in the FCI is hard to deal with in the traditional grid method. In this paper, an improved multiphase smoothed particle hydrodynamics (SPH) algorithm corrected with the kernel gradient correction (KGC) technique is presented for multiphase flow with a large density ratio and complex interfacial behaviors. The density discontinuity across the multiphase interface is described with the use of special volume, which only depends on the position information of adjacent particles. This multiphase SPH algorithm, which is troubled by an unstable and mixed-interface problem under a large density ratio, is significantly improved with the KGC technique. The accuracy and robustness of the improved method are demonstrated in the numerical simulations of the deformation of a square droplet, Rayleigh–Taylor instability, and bubble rising in water. The verified corrected multiphase SPH is applied to simulate the hydrodynamic behaviors of the general FCI and the interaction between fuels coated with stainless steel film and coolant. Boundary layer stripping, Rayleigh–Taylor instability, and Kelvin–Helmholtz instability are observed as important mechanisms of hydraulic fracturing. The fragments’ distribution and the influence of stainless steel film are analyzed. The existence of a stainless steel film has been shown to inhibit breakage.

Numerical investigation and experimental study on fracture processes of central flawed sandstone Brazilian discs

The propagations and connections of rock mass fissures are direct factors that lead to failure of rock engineering structures. Based on this, the traditional kernel function in the smoothed particle hydrodynamics (SPH) method was improved, which could simulate the progressive propagation processes of rock fissures. Brazilian disc samples of red sandstone with different fissure angles were prepared, and experiments on the crack propagations of Brazilian discs under uniaxial compression were carried out combined with digital image correlation technology. The results show that when the inclination angle of the prefabricated fissure is 0°, cracks initiate from the middle of the fissure and propagate along the loading direction; “Wing cracks” occur at prefabricated fissure inclination angles of 30°∼60°; when the inclination angle is 90°, cracks propagate along the direction of the prefabricated fissure. The peak load of the samples first decreases and then increases with increasing inclination angle, and was minimum when the angle was 60°. An improved SPH algorithm was used to simulate the crack growth of Brazilian discs with different fissure angles, and the simulation results are consistent with the experimental results, which verifies the rationality of the proposed method. However, most rock engineering problems are three-dimensional, so future research directions should focus on the development of 3D SPH parallel programs.

An SPH stress correction algorithm based on the quartic piecewise smooth kernel function

<p indent="0mm">Smoothed particle hydrodynamics (SPH) is a popular adaptive Lagrangian mesh-free particle method. For the tensile instability problem in traditional SPH, according to the sufficient condition of tensile instability, a new quartic piecewise smooth kernel function with non-negative second derivative is proposed, and an SPH stress correction algorithm is obtained in this study. The numerical results show that the modified SPH algorithm can effectively describe the formation processes of 2D and 3D vdW liquid drops. Then, based on the modified SPH algorithm, the effects of different physical parameters on the particle distribution of 2D circular droplets are further discussed. The results show that, with the appropriate temperature or initial particle spacing, the boundary particles of circular droplets are neither clustered nor scattered, and as the fluid temperature or initial particle spacing increases, the boundary particles will be scattered. Conversely, the particle distribution of circular droplets becomes more uniform with the increase in the smooth length proportion coefficient.

Development of smoothed particle hydrodynamics method for modeling active nematics

AbstractThis article proposes a novel graphics processing unit‐based active nematic flow solver based on the smoothed particle hydrodynamics (SPH) method. Nematohydrodynamics equations are discretized using the SPH algorithm. Flow behavior, nematic ordering, topological defects, and vorticity correlation are calculated and discussed in detail. The spectrum of the kinetic energy with respect to the wavenumber is calculated at high particle resolution, and its slope at the different length scales is discussed. To exploit the SPH capabilities, pathlines of nematic particles are evaluated during the simulation. Finally, the mixing behavior of the active nematics is calculated as well and described qualitatively. The effects of two important parameters, namely, activity and elastic constant are investigated. It is shown that the activity intensifies the chaotic mixing nature of the active nematics, while the elastic constant behaves oppositely.

Research on water entry problems of gas-structure-liquid coupling based on SPH method

The study on the dynamic response of deformable structure when it enters into the water is crucial for the stability and safety evaluation of structure. As a Lagrangian particle method, SPH (Smoothed Particle Hydrodynamics) has unique advantages in dealing with the free surface, multi-phase flow, and large deformation. So, this paper attempts to establish a unified SPH algorithm to study the coupling of deformable structure and multi-phase flow problem. Firstly, the strategies to eliminate the tensile instability in the gas phase, are put forward to ensure calculational stability. Moreover, the Riemann model between different materials is established to get a robust gas-structure-liquid contact algorithm, and the corresponding contact algorithm is presented. Finally, the water entry of an elastic wedge is simulated, and the elastic features of the water entry are revealed. The strategies to eliminate the tensile instability and the Riemann contact algorithm also demonstrate constructive effects. By comparing the results of the two-phase/three-phase water entry models, the effect of air on the dynamic response of the elastic wedge is analyzed. Moreover, the effects of the parameters such as elastic modulus, deadrise angle and air's dissipation are discussed to provide a reference for structural design in engineering.

Dynamical response of a floating plate to water waves using a smoothed particle hydrodynamics algorithm for nonlinear elasticity

In this work, a newly developed Smoothed Particle Hydrodynamics (SPH) algorithm for nonlinear elasticity is combined with an incompressible SPH fluid solver to investigate the dynamics of a floating plate under impacts of regular water waves with a high steepness. Two scenarios of the plate's rigidity are investigated. The simulation results show that deformations of the stiffer plate mainly occur in a simple bending mode with small amplitudes, and the plate is almost submerged by a strong fluid flow over its surface. In the other scenario, the plate deforms more complexly with much higher deformation amplitudes but experiences a much weaker overwash. The more flexible plate is less resistant to wave motions and converts more wave energy into elastic deformations, and therefore, the overwash is less severe. A strong overflow exerts a pressure force onto the plate that alters the plate's dynamics and adds a viscous (damping) effect on the plate's elastic vibrations, especially in high-frequency modes. A rigorous examination of the numerical convergence and validation using the linear thin plate theory is also carried out. The new SPH algorithm for nonlinear elasticity shows its stability and reliability in evaluating finite and large elastic deformations. Therefore, it is promising for simulating elastic structures in fluid–structure interaction problems.