Smoothed Particle Hydrodynamics Method Research Articles

Improving approximation accuracy in Godunov-type smoothed particle hydrodynamics methods

The study examines the origin of errors resulting from the approximation of the right hand sides of the Euler equations using the Godunov type contact method of smoothed particle hydrodynamics (CSPH). The analytical expression for the numerical shear viscosity in CSPH method is obtained. In our recent study the numerical viscosity was determined by comparing the numerical solution of momentum diffusion in the shear flow with theoretical one. In this study we deduce the analytical expression for the numerical viscosity which is found to be similar to numerical one, confirming the obtained results. To reduce numerical diffusion, diffusion limiters are typically applied to expressions for contact values of velocity and pressure, as well as higher-order reconstruction schemes. Based on the performed theoretical analysis, we propose a new method for correcting quantities at interparticle contacts in CSPH method, which can be easily extended to the MUSCL-type (Monotonic Upstream-centered Scheme for Conservation Laws) method. Original CSPH and MUSCL-SPH approaches and ones with aforementioned correction are compared.

Dynamic Load Balancing of Multi-GPU Parallelization for VULCANO VE-U7 Corium Spreading Analysis Using SOPHIA

The SOPHIA code is a graphical processing unit (GPU)–based smoothed particle hydrodynamics (SPH) framework for fundamental nuclear thermal-hydraulic and safety applications developed by Seoul National University. Focusing on particle-based SPH methods, the SOPHIA code provides capabilities for computational fluid dynamics–level analysis in addressing complex multiphase and multiphysics issues related to severe accidents and reactor safety. Since the SPH method requires high computational cost due to the nature of the particle-based method, the SOPHIA code was parallelized with multiple GPUs. However, using multiple GPUs may cause load imbalance as particles migrate between GPUs, which degrades performance. In this study, we developed a dynamic load-balancing algorithm to increase computational efficiency by reducing the load imbalance. Additionally, a novel cumulative time comparison approach is proposed as a criterion for adjusting boundaries between GPUs, ensuring low load imbalance. To evaluate the performance of the algorithm, three-dimensional dam-break simulations were conducted. The results demonstrated enhanced computational efficiency and equitable load distribution among GPUs compared to using fixed subdomains. Additionally, the developed algorithm was utilized to analyze the VULCANO VE-U7 experiment, and the results were well aligned with the experimental data. Therefore, the practical applicability of the proposed dynamic load-balancing algorithm in nuclear safety analyses has been confirmed.

Numerical Simulation of a Shed-Tunnel Structure’s Dynamic Response to Repeated Rockfall Impacts Using the Finite Element–Smoothed Particle Hydrodynamics Method

In practical engineering, a shed-tunnel structure often encounters repeated impacts from rockfall during its whole service life; therefore, this research focuses on exploring the dynamic response characteristics of shed-tunnel structures under repeated impacts from rockfall with a numerical method. First of all, based on a model test of a shed tunnel under rockfall impacts as a reference, an FEM (finite element method)-SPH (Smoothed Particle Hydrodynamics) coupled numerical calculation model is established based on the ANSYS/LS-DYNA finite element code. Numerical simulation of the dynamic response of the shed-tunnel structure under rockfall impacts is realized, and the rationality of the model is verified. Then, with this model and the full restart technology of the LS-DYNA code, the effects of four factors, e.g., rockfall mass, rockfall impact velocity, rockfall impact angle and rockfall shape, on the impact force and impact depth of the buffer layer, the maximum plastic strain and axial force of the rebar, the shed roof’s vertical displacement and plastic strain of the shed tunnel are studied. The results show that the impact force, impact depth, roof displacement and plastic strain of the shed tunnel are positively correlated with the rockfall mass, velocity and angle under multiple rockfall impacts. The impact force, roof displacement and plastic strain of the shed-tunnel structure generated by the impact of rockfall consisting of cuboids are all greater than those under spherical rockfall, and the impact depth generated by the impact of spherical rockfall is greater than that of rockfall consisting of cuboids. For rockfall consisting of cuboids, the impact depth, roof displacement and plastic strain are negatively correlated with the contact area. Under repeated rockfall impacts, the peak impact force usually increases first and then tends to be stable.

Numerical simulation study of aluminum particle evaporation combustion process based on SPH method

A large variety of metal fuels is usually added to the modern solid rocket propellants to improve the propellant energy and motor specific impulse and to suppress high frequency unstable combustion. Among them, aluminum is the most common additive. The combustion process of aluminum can significantly affect the combustion characteristics of a solid rocket motor. In this paper, the SPH (Smoothed Particle Hydrodynamics) method is used to simulate the combustion process of aluminum particles. First, the SPH discrete equations with an evaporation combustion model are derived. On this basis, the evaporation combustion process of aluminum particles is numerically simulated. The results show that when aluminum particles are heated and evaporated in a static flow field, an alumina shell will be formed on the surface, and further thermal expansion will cause the alumina shell to break. The molten aluminum will spray out, and an aluminum cap will be formed on the surface. The “microburst process” will be similar to the gel droplet. In the convective environment, the flame structure of aluminum particles will be obviously peach shaped, which will wrap aluminum particles at the bottom. The simulation results are consistent with the experimental results.

Performance of Ergun’s Equation in Simulations of Heterogeneous Porous Medium Flow with Smoothed-Particle Hydrodynamics

The flow of water through a channel with a heterogeneous porous layer in its central core is simulated using the method of Smoothed-Particle Hydrodynamics (SPH). Three different porous substrates are considered that differ in the geometry of their grain arrays. The heterogeneity is modeled by dividing the porous substrate into four zones that each have a different porosity. The pressure loss and the flow across the channel are simulated at two different scales, the pore scale and the Representative Elementary Volume (REV) scale, based on use of the Ergun equation. Since the computational cost at the REV scale is much lower than at the pore scale, it is therefore important to assess how accurately the REV-scale calculation reproduces the pore-scale results. The REV-scale simulation predicts cross-sectional mainstream velocity profiles and head losses through the channel that differ from the pore-scale results by root-mean-square errors of about 0.01% and 0.3%, respectively.

Simulating 2D Fluid Motion with the Smooth Particle Hydrodynamic Approach

Abstract Virtual two-dimensional (2D) fluid simulation is useful for directly simulating fluids in various situations, including geological simulations for landslides and fluid simulations for teaching. This research aims to simulate the behaviour of three different types of fluids (water, coconut oil, and glycerine) in a 2D container and analyse how these three types of fluids behave under various conditions, including interactions with boundaries. The research used Python programming to simulate fluids and the Wondershare Filmora X application to combine images. The Smooth Particle Hydrodynamics method simulated fluid in a 2D container with 10,000 particles by deriving the force density field directly from the Navier-Stokes equations. The Navier-Stokes equations were utilized to find the acceleration and velocity of fluid particles by considering external forces, internal forces, and gravity through this method. Acceleration and velocity were validated due to wall collisions, collisions with boundaries, and collisions between particles, which caused changes in particle position and velocity. During visualization, the fluid velocity decreased over time due to attenuation caused by interactions between neighbour particles, particles with boundaries, and particles with walls. From the simulation, it was observed that the fluid flowed from a higher place to a lower place, with fluid particles taking the shape of the container and the surface of the fluid forming waves. On the other hand, simulations with boundaries indicated that smaller gap sizes and higher viscosities led to increased difficulty in fluid penetration into the gap within the container.

Study on the attenuation pattern of stress wave in granite impacted by 30CrMnSiA alloy steel projectiles at 1.5–5.5 km/s

The damage ability of hypervelocity kinetic energy projectile penetrating ground has become a hotspot in modern military research. In this study, a hypervelocity impact test on a granite target subjected to projectiles using a two-stage light gas gun is conducted to study the stress wave evolution in granite under hypervelocity penetrations. The parameters of the *MAT_JOHNSON_HOLMQUIST_CERAMICS(JH-2) constitutive equation are calibrated using the results of the splinter impact test and the static test, and numerical simulations are performed using the smoothed particle hydrodynamics method coupled with finite element method (SPH-FEM coupled method) to extend the resulting data. A formula for calculating the stress wave peak attenuation is established, indicating that the maximum impact pressure produced by the hypervelocity impact decreases exponentially with scaling distance, and the attenuation coefficient is related to the degree of rock damage. Additionally, the attenuation of the speed of sound is used to characterize rock damage, and the damage deterioration law of granite under hypervelocity impact is analyzed based on the damage factor.

A smoothed particle hydrodynamics method for two-phase electrohydrodynamics modeling with Nernst–Planck equations

The widely used leaky dielectric model often overlooks the rate of change in electric charges, leaving the impact of the charge conservation mechanism on two-phase electro-hydrodynamics (EHD) flows inadequately explored. In this study, we address this gap by introducing a charge-conservative model (CCM) for simulating such EHD systems within the framework of the smoothed particle hydrodynamics (SPH) method. Our methodology employs a fully explicit incompressible SPH (EISPH) approach to discretize the pressure Poisson, the electric potential Poisson, and the Nernst–Planck (N–P) equations. This work presents two notable contributions: (i) the introduction of the charge-conservative model into the incompressible SPH framework and (ii) the achievement of its discretization through a fully explicit methodology. To validate the proposed CCM, we conduct a comprehensive comparison with analytical solutions, as well as existing numerical and experimental results. The results affirm that the CCM consistently produces accurate outcomes across various test cases.

Investigation of smoothed particle hydrodynamics (SPH) method for modeling of two-phase flow through porous medium: application for drainage and imbibition processes

The drainage and imbibition processes are critical mechanisms in petroleum engineering. These processes in a porous medium are controlled by surface forces and pressure gradients. The study of these processes in the pore scale by common simulators always has limitations in multiphase flow modeling. Also, obtaining relative permeability curves through laboratory analysis requires expensive equipment. Additionally, these laboratory experiments are quite expensive and may introduce significant uncertainties. For this purpose, this study investigated the creation of relative permeability curves and their effect on oil production. Initially, single-phase fluid and two-phase droplet flow within a fracture with both soft and rough surfaces were utilized to validate the formulation of the Smoothed Particle Hydrodynamics (SPH) method. Then, by using three randomly constructed porous medium models, the imbibition and drainage processes have been studied. Finally, sensitivity study has been carried out on critical parameters related to fluid flow dynamics in the porous environment, including pressure changes, wettability, and heterogeneity in drainage and imbibition processes. The simulation results were consistent with current theories; therefore, it is reasonable to consider SPH to characterize the fluid flow dynamic during the drainage and imbibition processes. According to sensitivity studies, pressure gradient (residual saturation of displaced fluid is about 5.65% and 8.44%) and heterogeneity (the residual saturation of the displaced fluid was 4.04% and 2.98%) have the largest impact on flow modeling in both drainage and imbibition processes and wettability (the residual saturation became 36.62% and 5.12%) has significant effect on the drainage process through porous medium. In general, fluid flow dynamic studies can be performed using the SPH method to model fluid flow in simple and complex porous medium under various flow conditions. The SPH method can also be used as an applicable tool to investigate the hydrocarbon fluids flow within larger geometries in the future.

Two approaches for constructing multivariate injection models for prefilming airblast atomizers

More realistic droplet starting conditions for Euler–Lagrangian simulations enable e.g. more precise soot prediction in jet engines. Up to now, mainly the droplet size distribution of sprays is considered, but not the multivariate dependence structure of droplet size, starting position and initial velocity. A novel concept for extracting multivariate spray data efficiently from detailed simulations of the atomizing process into high fidelity Euler–Lagrangian simulations of spray combustion is presented in this paper. Therefore, simulations of a prefilming airblast atomizer using the Smoothed Particle Hydrodynamics method are considered. The multivariate dependence structure in the spray is identified using rank transformation. Two models of different nature are proposed which are able to reproduce the multivariate dependence structure. The first model follows a data-driven approach using vine copulas and marginal distributions. In contrast, the second model is based on human knowledge and assumptions enabling deeper insights into the atomization process. Both models demonstrated to reproduce the multivariate character of the spray data effectively. An assessment of their capabilities reveals that the first model might be more suitable for spray data of annular injectors.

Hypervelocity impact against aluminium Whipple shields in the shatter regime with systematic parameter variation: An experimental and numerical study

Aluminium Whipple shields are commonly used to protect spacecraft against hypervelocity impacts (HVIs) from orbital debris and micrometeoroids. Since numerical models nowadays are vital in the design process of protective shields, experimental studies of HVI are important to ensure that the numerical methods are robust and capable of accurately describing a range of impact conditions and material responses. The shatter regime is the transition velocity range between ballistic impact and hypervelocity impact, typically defined from 3 to 7 km/s. In this region, the debris cloud generated by the impact transitions from a few large, solid fragments at the lower end of the velocity range, to a high number of smaller fragments and partial melting of the projectile at the higher velocities. In this study, an experimental campaign of 22 normal impacts of spherical AA1100 projectiles on AA6061-T6 Whipple shields is performed, where the impact velocity and bumper thickness are systematically varied to study the change in debris cloud characteristics and shield damage. Impact velocities from 2.6 to 5.0 km/s are investigated, combined with bumper thicknesses of 1.0, 1.5 and 2.0 mm. Analysis of the experimental results is conducted using high-speed camera footage of the debris clouds and post-impact analysis of bumpers and rear walls. A numerical model is then established using the Smoothed Particle Hydrodynamics (SPH) method in the IMPETUS Solver, and the numerical results are compared to the experimental data. The simulations are able to capture the main trends found in the experimental study, and show a similar level of damage as the experiments when varying the impact velocity and bumper thickness. The simulations have somewhat smaller fragments generated in the debris cloud than in the experiments, leading to slightly less damage inflicted on the rear wall.

Applications and Prospects of Smooth Particle Hydrodynamics in Tunnel and Underground Engineering

Smoothed particle hydrodynamics (SPH) is a state-of-the-art numerical simulation method in fluid mechanics. It is a novel approach for modeling and comprehending complex fluid behaviors. In contrast to traditional grid-dependent techniques like finite element and finite difference methods, SPH utilizes a meshless, purely Lagrangian approach, offering significant advantages in fluid simulations. By leveraging a set of arbitrarily distributed particles to represent the continuous fluid medium, SPH enables the precise estimation of partial differential equations. This grid-free methodology effectively addresses many challenges associated with conventional methods, providing a more adaptable and efficient solution framework. SPH’s versatility is evident across a broad spectrum of applications, ranging from advanced computational fluid dynamics (CFD) to complex computational solid mechanics (CSM), and proves effective across various scales—from micro to macro and even astronomical phenomena. Although SPH excels in tackling problems involving multiple degrees of freedom, complex boundaries, and large discontinuous deformations, it is still in its developmental phase and has not yet been widely adopted. As such, a thorough understanding and systematic analysis of SPH’s foundational theories are critical. This paper offers a comprehensive review of the defining characteristics and theoretical foundations of the SPH method, supported by practical examples derived from the Navier–Stokes (N-S) equations. It also provides a critical examination of successful SPH applications across various fields. Additionally, the paper presents case studies of SPH’s application in tunnel and underground engineering based on practical engineering experiences and long-term on-site monitoring, highlighting SPH’s alignment with real-world conditions. The theory and application of SPH have thus emerged as highly dynamic and rapidly evolving research areas. The detailed theoretical analysis and case studies presented in this paper offer valuable insights and practical guidance for scholars and practitioners alike.

Numerical Study on the Breaking Bow Wave of High-speed KCS Model based on Smoothed Particle Hydrodynamics Method

Numerical Study on the Breaking Bow Wave of High-speed KCS Model based on Smoothed Particle Hydrodynamics Method

Semi‐implicit Lagrangian Voronoi approximation for the incompressible Navier–Stokes equations

AbstractWe introduce semi‐implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi‐implicit time marching schemes with the robustness of time‐dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection‐based Arbitrary‐Lagrangian‐Eulerian schemes, we need no remapping stage. A semi‐implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence‐free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi‐phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no‐slip and free‐slip boundary conditions.

Optimization of relief hole blasting satisfying synergistic constraints of rock-breaking area and hole-bottom minimum burden

A strategy to optimize relief hole positions is proposed to enhance the effectiveness of tunnel blasting in rock breaking. This study employed two predefined arithmetic progressions to coordinate the distribution of rock-breaking areas and hole-bottom minimum burdens allocated to each row of holes. Iterative calculations were performed to determine the final position of each row of holes. To determine the optimal drilling scheme, modeling and simulation were conducted using a finite element method-smoothed particle hydrodynamics (FEM-SPH) coupling algorithm. This approach allowed for a comparison of the rock-breaking effects of relief holes under different constraint combinations. This study indicates that the displacement of rock particles varies in different depth zones. The largest displacements of the rock particles were observed in the middle of the charge section. For a conventional working face with a width of 12.2 m and a designed advance of 3 m, the rock-breaking efficiency is optimal when the two control ratios, rA and rW, are 1.5 and 1.4, respectively. This study advances the underground blasting design technology and contributes to energy reduction and efficiency improvements in blasting engineering.

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.

Numerical simulation of manta ray swimming using a smoothed-particle hydrodynamics method and investigation of the vortical structures in the wake

A three-dimensional smoothed-particle hydrodynamics (SPH) method is used to study the moving boundary problem of a swimming manta ray, focusing on Eulerian and Lagrangian coherent structures. The manta ray's boundary motion is predefined by a specific equation. The calculated hydrodynamic results and Eulerian coherent structures are compared with data from the literature. To improve computational stability and efficiency, the δ+-SPH model used in this study incorporates tensile instability control and an improved adaptive particle-refinement technique. By comparing and analyzing the Eulerian and Lagrangian coherent structures, the relationship between these vortex structures and hydrodynamic force generation is examined, revealing the jet mechanism in the manta ray's wake. The SPH method presented herein is robust and efficient for calculating biomimetic propulsion problems involving moving boundaries with large deformations, and it can accurately identify vortex structures. The approach of this study provides an effective simulation tool for investigating biomimetic propulsion problems such as bird flight and fish swimming.

Modeling and experiment for the roller hemming of variable curvature aluminum alloy panel with adhesive

The autobody closures have high requirements on the appearance accuracy of A-class surfaces, smooth contours, and continuous edges, so the forming quality of the autobody closures has long been the center of attention in the roller hemming process. To facilitate weight reduction in automotive manufacturing, lightweight materials such as aluminum alloy and hemming adhesive are commonly used. However, the heterogeneous coupling effect between the adhesive and aluminum alloy panel during roller hemming can significantly influence the forming quality of the panel. Additionally, the precision of the roller posture and trajectory plays a crucial role in determining the final quality of the panels, given the complex geometry of the autobody closures. Therefore, in order to continuously improve the forming quality of the autobody closures, this paper investigates the roller hemming process applied to variable curvature panel with adhesive on autobody doors. Firstly, the kinematic model for the roller posture and trajectory during roller hemming of the curved surface-curved edge panel was developed based on differential geometry theory. Secondly, a simulation model for roller hemming of the panel with adhesive was established using the finite element method and the smoothed particle hydrodynamics method (FEM-SPH). The validity of the simulation was confirmed by comparing the simulated results with experimental outcomes. In the experiment, the algorithm for solving the posture and trajectory of the roller was applied, and the forming quality of the panel was evaluated by using the two indexes of roll-in/out coefficient and surface wave coefficient. Thirdly, the impact of the hemming factors on surface wave and roll-in/out was analyzed using the response surface methodology, leading to the development of a mapping relationship between the hemming factors and forming quality. This study provides valuable support for predicting the forming quality of variable curvature panels with adhesive and continuously improving the forming quality of autobody closures in the roller hemming manufacturing process.

An improved smoothed particle hydrodynamics method for modeling multiphase flows

Multiphase flows are prevalent in both natural and engineered systems. The study of multiphase flow problems using numerical simulation is challenging due to the presence of high nonlinearities and moving interfaces. In this paper, an improved multiphase smoothed particle hydrodynamics (SPH) model is proposed for simulating multiphase flows. In the improved multiphase SPH model, an improved interface repulsive force model is proposed to reduce the interpenetration of particles at the multiphase interface and make the multiphase interface smooth and clear, and an improved kernel gradient correction is introduced to optimize the computational results. In addition, the particle shifting technology is applied to make the particle distribution uniform. Five numerical examples including the Rayleigh–Taylor instability, non-Boussinesq lock-exchange problem, square droplet deformation, single bubble rise, and circular droplet oscillation are investigated to verify the correctness and effectiveness of the improved multiphase SPH model. The results demonstrate that the improved multiphase SPH approach is effective in modeling multiphase flows.

Gaussian smoothed particle hydrodynamics: A high-order meshfree particle method

Smoothed particle hydrodynamics (SPH) has attracted significant attention in recent decades, and exhibits special advantages in modeling complex flows with multiphysics processes and complex phenomena. Its accuracy depends heavily on the distribution of particles, and will generally be lower if the particles are distributed non-uniformly. A high-order SPH scheme is proposed in the present work for simulating both compressible and incompressible flows. It uses a Gaussian quadrature rule to perform the particle approximation of SPH by introducing Gaussian nodes. Unfortunately, the Gaussian nodes hardly overlap with SPH particles due to the Lagrangian feature, and thus we use a high-order interpolation method to obtain the corresponding physical quantities at the Gaussian nodes. The accuracy and robustness of the proposed Gaussian SPH are demonstrated by several numerical tests, including the Sod problem, Poiseuille flow, Couette flow, cavity flow, Taylor–Green vortex and dam break flow, and a convergence analysis is also conducted to evaluate the effects of particle resolution and distribution for reconstructing a given function. The simulation results for each test case are in good agreements with the available analytical, experimental or numerical results, showing that the proposed Gaussian SPH method is accurate and reliable but expensive for simulating compressible and incompressible flow problems.