Smoothed Particle Hydrodynamics Research Articles

Metal-silicate mixing in planetesimal collisions

Impacts between differentiated planetesimals are ubiquitous in protoplanetary discs and may mix materials from the core, mantle, and crust of planetesimals, thus forming stony-iron meteorites. The surface composition of the asteroid (16) Psyche represents a mixture of metal and non-metal components. However, the velocities, angles, and outcome regimes of impacts that mixed metal and silicate from different layers of planetesimals are debated. Our aim is to investigate the impacts between planetesimals that can mix large amounts of metal and silicate, and the mechanism of stony-iron meteorite formation. We used smooth particle hydrodynamics to simulate the impacts between differentiated planetesimals with various initial conditions that span different outcome regimes. In our simulations, the material strength was included and the effects of the states of planetesimal cores were studied. Using a statistical approach, we quantitatively analysed the distributions of metal and silicate after impacts. Our simulations modelled the mass, depth, and sources of the metal-silicate mixture in different impact conditions. Our results suggest that the molten cores in planetesimals could facilitate mixing of metal and silicate. Large amounts of the metal-silicate mixture could be produced by low-energy accretional impacts and high-energy erosive impacts in the largest impact remnant, and by hit-and-run and erosive impacts in the second-largest impact remnant. After impact, most of the metal-silicate mixture was buried at depth, consistent with the low cooling rates of stony-iron meteorites. Our results indicate that mesosiderites potentially formed in an erosive impact, while pallasites potentially formed in an accretional or hit-and-run impact. The mixing of metal and non-metal components on Psyche may also be the result of impacts.

Improved Smoothed Particle Hydrodynamics for the Three-Dimensional Solid Impact Problems

Total Lagrangian-Smoothed Particle Hydrodynamics (TL-SPH) method is an important method to improve the tensile instability of traditional SPH, but it still faces some defects, such as insufficient accuracy at boundary region, difficulty in obtaining damage and applying interface conditions. Therefore, the high-order TL-SPH is applied for the elastic–plastic solid. A damage model is proposed by adaptively transforming the type of kernel function. Furthermore, a Riemann contact algorithm is introduced for different solids. The advantages of the methods in improving tensile instability and simulating damage are verified by the cases of the plates and the notched beams with an impact load.

A comparative study on waveform prediction between SPH and S-ALE methods in impact welding

To explore the optimal method for simulating impact welding, we compared detailedly the smoothed particle hydrodynamics (SPH) and structured arbitrary Lagrangian-Eulerian (S-ALE) methods in predicting bonding interface. Based on the experimental results of Cu-Q235 steel atmospheric explosive welding, an in-depth analysis was presented. The results show that the SPH and S-ALE methods converged at element sizes of 2.5 and 2 μm, respectively. When the element size was further reduced to 0.5 % of the wavelength, the errors of both methods were less than 5 %. Benefiting from the gradient mesh, the efficiency of the S-ALE method was 2–4 times that of the SPH method at the same element size. With the addition of the gas medium, the S-ALE method derived the formation mechanism of the gap gas shockwave and indicated that the pressure distribution is not uniform. Furthermore, the local high pressure of the gas shockwave prevents the vortex closure during the wave formation, generating the pore. The calculated pressure and velocity of the wavefront were 20 MPa and 3500 m s−1, respectively. In conclusion, the SPH is suitable for fast previewing waveform interfaces, while the S-ALE method has the advantage of capturing fine waveform structures under various environmental conditions.

The simulation of droplet impact on liquid film evaporation in horizontal falling film evaporator based on smoothed particle hydrodynamics

Purpose In this paper, the complex flow evaporation process of droplet impact on the liquid film in a horizontal falling film evaporator is numerically studied based on smoothed particle hydrodynamics (SPH) method. The purpose of this paper is to present the mechanism of the water treatment problem of the falling film evaporation for the high salinity mine water in Xinjiang region of China. Design/methodology/approach To effectively characterize the phase transition problem, the particle splitting and merging techniques are introduced. And the particle absorbing layer is proposed to improve the nonphysical aggregation phenomenon caused by the continuous splitting of gas phase particles. The multiresolution model and the artificial viscosity are adopted. Findings The SPH model is validated qualitatively with experiment results and then applied to the evaporation of the droplet impact on the liquid film. It is shown that the larger single droplet initial velocity and the smaller single droplet initial temperature difference between the droplet and liquid film improve the liquid film evaporation. The heat transfer effect of a single droplet is preferable to that of multiple droplets. Originality/value A multiphase SPH model for evaporation after the droplet impact on the liquid film is developed and validated. The effects of different factors on liquid film evaporation, including single droplet initial velocity, single droplet initial temperature and multiple droplets are investigated.

Essentially non-hourglass SPH elastic dynamics

More than two decades ago, the numerical instabilities of particle clustering and non-physical fractures encountered in the simulations of typical elastic dynamics problems using updated Lagrangian smoothed particle hydrodynamics (ULSPH) was identified as tensile instability. Despite continuous efforts in the past, a satisfactory resolution for the simulations of these problems has remained elusive. In this paper, the concept of hourglass modes, other than tensile instability, is first explored for the discretization of shear force, arguing that the former may actually lead to the numerical instabilities in these simulations. Based on such concept, we present an essentially non-hourglass formulation by utilizing the Laplacian operator which is widely used in fluid simulations. Together with the dual-criteria time stepping, adopted into the simulation of solids for the first time to significantly enhance computational efficiency, a comprehensive set of challenging benchmark cases is used to showcase that our method achieves accurate and stable SPH elastic dynamics.

IGA-SPH: coupling isogeometric analysis with smoothed particle hydrodynamics for air-blast–structure interaction

IGA-SPH: coupling isogeometric analysis with smoothed particle hydrodynamics for air-blast–structure interaction

Correction to: Hyperbolic conduction: A fast, physical conduction model implemented in Smoothed Particle Hydrodynamics

Correction to: Hyperbolic conduction: A fast, physical conduction model implemented in Smoothed Particle Hydrodynamics

Improvement in the Accuracy and Efficiency of Smoothed Particle Hydrodynamics: Point Generation and Adaptive Particle Refinement/Coarsening Algorithms

An adaptive particle refinement (APR) algorithm has been developed for the smoothed particle hydrodynamics (SPH) method to augment the resolution of the region of interest to achieve high accuracy and simultaneously reduce the cost of computational resources. It is widely applied in the field of fluid-controlling problems involving large interface deformations, such as the two-phase flow and fluid–structure interaction because this algorithm can capture the interface with high accuracy. Nonetheless, existing APR algorithms widely encounter computational dispersion issues at the interface of regions of different particle resolutions. Moreover, traditional shifting algorithms applied in the APR processes also have difficulties in dealing with particles with different smooth lengths. In this work, an algorithm for fast particle generation was first developed based on the accelerated ray method, which accelerates the discretization of the flow field into particles. Then, a dynamic refinement/coarsening algorithm based on the APR algorithm is proposed to solve the computational dispersion problem that occurs at the refinement/coarsening interfaces. In addition, the shifting algorithm was improved in this work to ensure the particles are always well distributed during numerical calculations and, thus, can efficiently facilitate the adaptive particle refinement/coarsening processes. Comparative analysis indicates that the robust algorithms developed for the SPH method in this work can lead to more precise and reasonable flow fields compared with the conventional SPH adaptive methods.

An improved algorithm for Finite Particle Method considering Lagrange-type remainder

The Finite Particle Method (FPM) is a significant improvement to the traditional Smoothed Particle Hydrodynamics method (SPH), which can greatly improve the computational accuracy of the entire computational domain. However, unstable calculation results and long computational time are still major obstacles to the development of FPM. Based on matrix decomposition, the fundamental equations of the traditional Finite Particle Method are rewritten and a Generalized Finite Particle Method (GFPM) is derived by introducing Lagrange-type remainder. By deriving and rewriting the fundamental equations, the GFPM method can be theoretically proven to be always stable. Numerical examples show that the GFPM method can utilize a smaller computational scale to achieve the same computational accuracy as the FPM method, with a corresponding reduction in computational time. Finally, the GFPM method is applied to a one-dimensional stress wave propagation problem and a one-dimensional heat conduction problem, and the computational results are compared with those of the SPH method and the FPM method, which verify that the GFPM has higher computational accuracy and stability.

Numerical simulation on in-vessel molten corium behavior with external vessel cooling using smoothed particle hydrodynamics

The in-vessel retention through external reactor vessel cooling (IVR-ERVC) strategy is a key management strategy for early termination of a nuclear severe accident that can threaten the integrity of the reactor vessel. To simulate the physical phenomena of the molten corium, the smoothed particle hydrodynamic (SPH) method is utilized in this study. The SPH method is a Lagrangian computational fluid dynamic (CFD) method that can simulate multi-fluid stratification, turbulence, natural circulation, radiative heat transfer, thermal ablation, and crust formation. To address the external vessel cooling, it is coupled with a conventional 1-D nuclear system analysis method. The 1-D system analysis code can calculate the two-phase natural circulation of cooling water and the convective heat transfer on the external reactor vessel wall. These two simulation codes exchange the temperature and heat flux of the reactor vessel outer wall. This study numerically simulated the IVR-ERVC strategy for a Korean high-power reactor and compared it with the traditional lumped parameter method (LPM). Unlike LPM, this study provides localized detailed data about the thermal hydraulic behavior of molten corium and visualization of phenomena in the IVR-ERVC strategy. This enhances our understanding of the phenomena in IVR-ERVC strategy and introduces new perspectives.

Coupling SPH-DEM method for simulating the dynamic response of breakwater structures under severe free surface flow

This paper introduces a novel smoothed particle hydrodynamics (SPH) - discrete element method (DEM) to enhance our understanding of the impact of free-surface flow on breakwater structures. SPH is employed to simulate incompressible fluids, while DEM is utilized to track the trajectories of solid particles. Advanced strategies including polyhedral particle modeling and contact model are adopted to enhance the model's capability in solving the dynamic behavior of irregular particle. Several cases are analyzed to validate the accuracy of coupling model, showing a high level of agreement. Additionally, the impact of wave flow on coastal breakwaters composed of irregular rocks is simulated. This work reveals that the coupling model effectively provides extensive information about the flow field and dynamic response of multi-particle systems, such as velocity, fluid force and force chain distribution. This model exhibits significant potential for analyzing the dynamic response of severe free surface flow on the multi-block structures.

Numerical simulation of freak wave generation and evolution process based on SPH method

With the occurrence of maritime accidents all over the world, the study of extreme waves has been promoted. These extreme waves are often called freak waves in the scientific community. At present, a variety of mechanisms are proposed to explain freak waves in the marine environment, such as directional focusing, dispersive focusing, and nonlinear modulation instability. At first, a hydrodynamic model is established based on the Smoothed Particle Hydrodynamics (SPH) method in the C# environment, and the regular wave generated by the piston wave generator is numerically simulated. Secondly, the simulation results were analyzed and visualized by using Paraview software, compared with physical experimental datas to verify the reliability of this model. Then, the generation and evolution of freak waves were numerically simulated through the movement of piston wave generators on both sides of a 2D numerical wave flume, and the influence of frequency and amplitude was analyzed by using directional focusing. The results show that if the frequency is smaller and the amplitude is larger, it is more likely to generate freak waves and wave-breaking phenomena. This study lays a foundation for the research of freak waves in the future.

Publisher's Note: “A modified weakly compressible smoothed particle hydrodynamics mixture model for accurate simulation of wave and porous structure interaction” [Phys. Fluids 36, 047128 (2024)

Publisher's Note: “A modified weakly compressible smoothed particle hydrodynamics mixture model for accurate simulation of wave and porous structure interaction” [Phys. Fluids <b>36</b>, 047128 (2024)

Forming Mercury from Excited Initial Conditions

Mercury is notoriously difficult to form in Solar System simulations, due to its small mass and iron-rich composition. Smooth particle hydrodynamics simulations of collisions have found that a Mercury-like body could be formed by one or multiple giant impacts, but due to the chaotic nature of collisions, it is difficult to create a scenario where such impacts will take place. Recent work has found more success forming Mercury analogues by adding additional embryos near Mercury’s orbit. In this work, we aim to form Mercury by simulating the formation of the Solar System in the presence of the giant planets Jupiter and Saturn. We test out the effect of an inner disk of embryos added on to the commonly used narrow annulus of initial material. We form Mercury analogues with core-mass fractions (CMFs) > 0.4 in ∼10% of our simulations, and twice that number of Mercury analogues form during the formation process but are unstable and do not last to the end of the simulations. Mercury analogues form at similar rates for both disks with and without an inner component, and most of our Mercury analogues have lower CMFs than that of Mercury, ∼0.7, due to significant accretion of debris material. We suggest that a more in-depth understanding of the fraction of debris mass that is lost to collisional grinding is necessary to understand Mercury’s formation, or some additional mechanism is required to stop this debris from accreting.

Extreme wave impacts on a suspended box above free surface

A systematic approach incorporating precision-controlled experiments and high-fidelity numerical simulations has been employed to delve deeper into the physics of extreme wave impact pressures. Using a suite of high-speed imaging and high-resolution pressure sensing techniques that are accurately synchronized with the wave generation, a consistent and well-correlated set of data providing details of the focusing incident wave front, flow velocities, and impact pressure time histories has been successfully obtained. The numerical simulations using a validated incompressible smoothed particle hydrodynamics (ISPH) provided further details that were not tractable in the experiments. Based on the results obtained, there were five broad impact scenarios identified, ranging from focusing crest impacts to plunging jet impacts with varying entrapped air. Among these impact types, the highest impact pressures were those associated with a focusing wave crest. It has been found that high impact pressures were correlated with a convergence of the horizontally impinging overturning crest and the vertical surge of the wall boundary water mass, but with the overturning crest impingement just ahead of the arrival of the wall boundary water mass, which in essence amounted to the impingement of a focusing wave front. Depending on the relative arrival times of the impinging crest and the wall boundary upsurge, the impact scenarios could vary from an up-slosh to a jet impingement with a clear entrapped air pocket, followed by a flip-through of the incident crest. For the scenario with the highest impact pressures, broadly classified as type II impact in this paper, the peak pressures could reach as high as 85ρC2, an order of magnitude higher than impact scenarios without the focusing effect, such as the scenario with a plunging jet impact with entrapped air (classified as types III and IV impact in this study). As the volume of entrapped air for this scenario was relatively small, the one-phase ISPH model used in this study was able to capture the peak pressure characteristics, including the peak pressure amplitudes. However, in scenarios with significantly highly entrapped air during impact, a two-phase model would be necessary.

Experimental and numerical study on the mechanism of interlayer explosive welding

Currently, a gap in understanding the mechanism of interlayer explosives exists. This study systematically investigated this mechanism using TP 270C/SUS 821L1 to fill this knowledge gap. By comparing the outcomes of direct and interlayer welding through methods such as optical microscope (OM), computed tomography (CT), electron probe micro-analysis (EPMA), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), nanoindentation, and tensile shear test, it was found that an interlayer can significantly lessen the energy at the target interface. This was further evident when comparing welds with varying interlayer thicknesses, showing that thinner interlayers lead to less energy transfer between the flying plate and the interlayers. Notably, at an interlayer thickness of 0.1 mm, the welding interface appeared irregular. The smoothed particle hydrodynamics (SPH) method was employed to simulate the welding, highlighting the interlayer's impact on factors like pressure, jet, temperature, and melting. This simulation also explained why the 0.1 mm interlayer had an irregular interface due to jetting affecting the welding between the flyer plate and interlayer. The study also analyzed the weldability window in interlayer explosive welding, noting how the interlayer influenced its upper and lower limits. The relation between interlayer thickness and the constant k in the lower limit was examined, along with the minimum velocity needed for the flyer plate to generate a jet VP. Their relationship satisfied exponential functions in the detonation velocity range of 1800–3000 m/s. This study thus established a link between traditional and interlayer explosive welding.

Monte Carlo Vortical Smoothed Particle Hydrodynamics for Simulating Turbulent Flows

AbstractFor vortex particle methods relying on SPH‐based simulations, the direct approach of iterating all fluid particles to capture velocity from vorticity can lead to a significant computational overhead during the Biot‐Savart summation process. To address this challenge, we present a Monte Carlo vortical smoothed particle hydrodynamics (MCVSPH) method for efficiently simulating turbulent flows within an SPH framework. Our approach harnesses a Monte Carlo estimator and operates exclusively within a pre‐sampled particle subset, thus eliminating the need for costly global iterations over all fluid particles. Our algorithm is decoupled from various projection loops which enforce incompressibility, independently handles the recovery of turbulent details, and seamlessly integrates with state‐of‐the‐art SPH‐based incompressibility solvers. Our approach rectifies the velocity of all fluid particles based on vorticity loss to respect the evolution of vorticity, effectively enforcing vortex motions. We demonstrate, by several experiments, that our MCVSPH method effectively preserves vorticity and creates visually prominent vortical motions.

Effect of corrugated steel angle on the damage characteristics and anti‐explosion performance of corrugated steel–concrete composite structures

SummaryA three‐dimensional refined numerical simulation model of a corrugated steel–concrete slab composite structure under contact explosion load was established by the finite element model and smoothed particle hydrodynamics(FEM‐SPH) coupling method to explore the anti‐knock properties of corrugated steel reinforced concrete slabs with different angles. The effects of corrugated steel angle on the dynamic response, damage evolution characteristics, damage mode, anti‐knock property, and propagation mechanism of the shock wave in the composite structure were investigated, and the damage prediction and anti‐knock property evaluation of the composite structure were carried out. The results show that the simulation results of the mid‐span displacement of the corrugated steel are consistent with the experimental results, and the maximum error is 2.3%, which verifies the effectiveness of the contact explosion simulation process. The mid‐span displacement, peak stress, acceleration at the center point, and energy absorption value of 90° corrugated steel are 17.9%, 70.5%, 88.6%, and 59.4% lower than those of 30° corrugated steel. The damage range of the composite structure gradually decreases with increasing angle of the corrugated steel. The failure volume of the concrete slab reinforced by corrugated steel with different angles decreases with increasing angle of the corrugated steel, and the energy absorption value of the composite structure increases with increasing of angle of the corrugated steel, mainly because the corrugated steel increases the number of reflections of the stress wave. The research results can provide a theoretical basis for the application of composite structures in the field of structural anti‐explosion protection.

Numerical Study on the Swimming and Energy Self-Sufficiency of Multi-Joint Robotic Fish

Energy is one of the primary challenges in the long-term operation of robotic fish. The research on combining wave energy-harvesting technology with robotic fish for energy supplementation is not extensive, and there is insufficient comprehensive analysis on energy harvesting from waves and energy costs during swimming. Therefore, the energy self-sufficiency of multi-joint robotic fish is investigated by employing the coupling method of smoothed particle hydrodynamics (SPH) and multi-body dynamics in this study. A reversible energy conversion mechanism is applied to the robotic fish, serving as a driving system during swimming and as a power take-off (PTO) system during energy harvesting. The energy costs of the multi-joint robotic fish under various undulation parameters (including amplitude, frequency, and body wavelength) are analyzed, along with an examination of the influence of the PTO system on energy harvesting. The results show that, compared to the undulation amplitude and body wavelength, the undulation frequency has the greatest impact on swimming efficiency and energy costs, with low-frequency swimming being advantageous for efficient energy utilization. Additionally, the damping coefficient of the PTO system directly affects energy-harvesting efficiency, with higher energy-harvesting power achievable with an optimal PTO system parameter. Through a comprehensive analysis of energy costs and energy harvesting, it is concluded that the achievement of energy self-sufficiency for multi-joint robotic fish in marine environments is highly feasible.

A parallel multi-resolution Smoothed Particle Hydrodynamics model with local time stepping

Smoothed Particle Hydrodynamics (SPH) model has exhibited remarkable efficacy in addressing strongly nonlinear large deformation problems. However, the expensive computational cost could limit its application. To address this, we propose a novel parallel multi-resolution SPH model with a local time step strategy. This model integrates the multi-resolution model with a Message Passing Interface-based parallelization framework, wherein subdomains discretize the computational domain at varying resolutions. Meanwhile, a local fourth-order Runge-Kutta time integration scheme is introduced, enabling different subdomains to use different time steps. Subdomains of varying resolutions are devoid of overlapping regions, and changes in particle resolution at interfaces are achieved through a dynamic strategy involving particle merging and splitting. Besides that, we conducted a comparative analysis of different SPH discretization formats concerning their impact on the accuracy of multi-resolution particle discretization. Finally, several numerical tests were conducted to validate the accuracy and efficiency of the present multi-resolution SPH model.