Mesh-free Smoothed Particle Hydrodynamics 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.

Exploring Wave–Vegetation Interaction at Stem Scale: Analysis of the Coupled Flow–Structure Interactions Using the SPH-Based DualSPHysics Code and the FEA Module of Chrono

Aquatic vegetation in the littoral zone plays a crucial role in attenuating wave energy and protecting coastal communities from hazardous events. This study contributes to the development of numerical models aimed at designing nature-based coastal defense systems. Specifically, a novel numerical application for simulating wave–vegetation interactions at the stem scale is presented. The numerical model employed, DualSPHysics, couples the meshfree Smoothed Particle Hydrodynamics (SPH) fluid solver with a structural solver to accurately capture the two-way interactions between waves and flexible vegetation. The proposed numerical model is validated against experimental data involving a submerged rubber cylinder representing an individual vegetation stem, subjected to regular waves. The results demonstrate excellent agreement in hydrodynamics, force transfer, and the swaying motion of the flexible cylinder. Importantly, the approach explicitly captures energy transfer between the fluid environment and the individual stem. The numerical results indicate persistent turbulent flow along the vegetation stem, even when its swaying speed matches that of the surrounding environment. This reveals the presence of vortex shedding and energy dissipation, which challenges the concept of passive swaying in flexible aquatic vegetation.

Mesh-free SPH modelling of sediment scouring and flushing considering grains transport and transformation

Sediment scour numerical simulation plays a critical role in the design of water-resistant foundation engineering, and this paper addresses a significant gap in most related studies, which often overlook the transformation of sediment and struggle to identify the actual riverbed obscured by yielding bed and suspended load. To tackle this challenge, a comprehensive sediment model based on the meshless Smoothed Particle Hydrodynamics (SPH) method was developed. Firstly, to enhance computational efficiency and mitigate the high cost of Fluid-Solid Interaction (FSI) between water and sediments, cohesionless sediment grains were modelled as non-Newtonian fluids, with yield strength determined according to a combined strength criterion. Subsequently, sediment transformation and identification were determined based on sediment particle velocity and shear stress, with the seepage force driving yield sediment particle motion at the interface. The effectiveness of this comprehensive sediment model was validated through comparison with three scour experiments. The results show better agreement between the model and experimental data, with a root-mean-square error of less than 2.17% in scour morphology simulation and successful identification of the actual post-scouring bed surface in each case. However, the free surface simulation in this model still exhibits slight error, with a root-mean-square error of less than 8.35%.

Application of mesh-free and finite element methods in modelling nano-scale material removal from copper substrates: A computational approach

This study explores the modelling methodology using mesh-free smoothed particle hydrodynamics (SPH) and finite element modelling (FE) techniques to simulate the AFM-based nano-scratching processes for advancing precision engineering in nanotechnology. Tip wear in nano machining substantially increases the tip radius, thereby influencing the material removal mechanism and subsequently affecting the quality of machined nanostructures. In this context, this study examines the effects of rake angle (the inclination of the main cutting edge to the plane perpendicular to the scratched surface), tip radius and scratching depth on cutting forces, groove dimensions, and deformed thickness. This was achieved by implementing an in-house SPH method based particle code employing a Lagrangian algorithm, and an FE model incorporating the dynamic explicit algorithm implemented (in ABAQUS) to carry out nano-scratching simulations. The investigation revealed that the cutting mechanism transitioned to ploughing when the scratching depth decreased to 30% of the tip radius for OFHC-Cu workpiece material machined with a diamond tip. The dominance of normal forces over cutting forces during scratching indicated the side flow of material in the vicinity of the tip radius under intense contact pressure. The ploughing mechanism exhibited more sensitivity at a higher negative rake angle of 60°. Increased scratching depth and tip radius led to more significant material deformation owing to the induction of higher cutting forces, with the maximum deformation thickness 3.6 times the tip radius. The simulated results demonstrated favourable concordance with the experimental data.

Droplet asymmetry bouncing on structured surfaces: A simulation based on SPH method

The impact of a liquid droplet onto a macro-structured super-hydrophobic surface, results in an asymmetric spreading-retraction process and a significant decrease in contact time. The process involves large deformation of droplets and evolution of surface morphology, so it is difficult to efficiently simulate using traditional grid-based methods. In this study, a numerical model is established using the mesh-free smoothed particle hydrodynamics (SPH) method to simulate the interaction of liquid droplets with solid surfaces exhibiting complex macro-textures. Leveraging the Lagrange nature of SPH, liquid droplets can be model using free surface boundary condition. The weakly compressible SPH formulation is employed to discretize the governing equations of liquid. Surface tension is captured by introducing an additional negative pressure term, inducing attractive forces among fluid particles. Kernel functions are carefully chosen to mitigate stress instability resulting from droplet spreading and retraction. The model is then applied to simulate the dynamic processes of droplets impact on flat and non-flat super-hydrophobic surfaces. The bouncing dynamics of droplets are investigated under varying conditions, including Weber number, size, and morphology of macro-scale surface structures. Our simulation results for contact time, maximum diameter, and droplet morphology align closely with experimental observations. The contact time of the droplet exhibits a dependency on its size and surface geometry, with a transition towards planar geometry diminishing asymmetric spreading effects. The findings highlight the significance of Weber number and cylinder diameter in determining contact time, providing insights for the design of optimized surface structures for specific droplet impact parameters. In addition, the use of a free-surface condition for modeling proved computationally efficient for 3D simulations. The model effectively reproduces nonlinear behaviors such as droplet spreading, splashing, and bouncing, highlighting the significant advantage of SPH in simulating such problems.

A dislocation density-based meshfree computational framework for solid phase processing

This work proposes a computational modeling framework capable of predicting the behavior of materials when subject to solid phase processing (SPP). A macroscopic dislocation density based constitutive model with internal state variables correlated to microscopic dislocation densities is incorporated into a meshfree smoothed particle hydrodynamics (SPH) framework able to handle large deformations and high temperatures typical of what a material undergoes during SPP. Unlike phenomenological constitutive models that typically neglect material microstructural contributions to macroscale response, the dislocation density based constitutive model improves significantly the predictivity of our modeling framework in a wider range of conditions and allows the multiscale material responses to be simulated simultaneously. With dislocation density based model parameters calibrated to AA1100-O aluminum test data, the generality of the proposed framework is tested on two SPP techniques, namely friction extrusion (FE) and friction stir processing (FSP). Simulation results with different process parameters are systematically validated by experimental data for both cases. The validated models are then used to elucidate the inherent physics associated with SPP by revealing the distributions of temperature, strain, strain rate, and dislocation density, stick-slip contact conditions, and heat generation rates. Model-predicted high dislocation density regions in the processed AA1100-O also agree well with the dynamically recrystallized grain refinement zones observed from experiments.

Numerical simulation of dry laser derusting process based on SPH method

Laser cleaning is an efficient, environmental-friendly, and non-contact surface treatment technology. Laser radiation and heating cause the surface material to heat up and gasify, separating it from the substrate. Traditional mesh-based numerical methods are difficult to effectively simulate the evolution of erosion crater and the splashing phenomenon. In this study, a meshfree method, the smoothed particle hydrodynamics (SPH) method, is used to establish the numerical model of the interaction between the laser beam and the targeted material and to investigate the removal process of the rust layer under different laser operating conditions. In consideration of the coupling effect of laser absorption, heat transfer, and material phase change, the SPH modeling procedure and corresponding numerical scheme for heat transfer and heat-absorption-induced phase change are introduced. Additionally, a surface particle detection algorithm and surface normal vector calculation method are proposed to accurately compute the complex surface geometry of the erosion crater, which realizes the dynamic coupling of laser-energy absorption and laser-beam direction. The established SPH model is then used to simulate the temperature distribution of the rust layer under the action of a laser beam, and the influence of laser energy, beam overlap rate, and beam direction on the removal efficiency is analyzed. This study applies the meshfree SPH method to the study of laser rust removal process, verifies the accuracy of the surface detection algorithm, captures the spatter behavior of material particles after phase change, and reflects the advantages of the meshfree method in solving such problems.

Numerical investigation of wave-induced flexible vegetation dynamics in 3D using a coupling between DualSPHysics and the FEA module of Project Chrono

Vegetation meadows in coastal waters are a key constituent of a future green defense package due to the ecosystem services they provide and the potential to attenuate wave energy. To numerically describe the vegetation dynamics under wave action, this paper presents a novel application of a numerical coupling for solving fluid–elastic structure interactions (FSI) problems involving ultra-thin elements in a 3-D environment. The extended two-way coupling employed in this work combines the mesh-free Smoothed Particle Hydrodynamics (SPH) method in the DualSPHysics code to solve the fluid flow, and the Finite Element Analysis (FEA) structural solver in Project Chrono to solve the structural dynamics. To represent the vegetation, a flexible structure based on the Euler–Bernoulli beam model is used. The beam element is embedded into the SPH domain using an envelope subdomain that is discretized using dummy boundary particles. As such, this dummy envelope serves as a decoupling interface for the geometrical properties of the structure, allowing for ultra-thin structures smaller than the initial inter-particle distance (dp). The numerical approach is validated against an experimental setup including a flexible blade swaying under the action of an oscillatory flow. The results demonstrate that the numerical model is able to resolve the wave–vegetation interaction problem. Furthermore, additional insights into the blade dynamics reveal that the swaying velocity increases linearly along the length, with the upper part swaying at a speed comparable to the fluid velocity while the stem remains relatively stationary. Additionally, the findings indicate that rigid vegetation experiences higher forces per unit length, and in systems with substantial swaying motion, energy dissipation predominantly occurs around the lower base of the vegetation.

SPH modeling of caisson stability on rubble-mound foundation under wave action

<p indent="0mm">The caisson breakwater is the representative protective structure in coastal and offshore zones, which is mainly composed of the reinforced concrete caisson and the rubble-mound foundation. The displacement and inclination of caisson structures are generally considered to be the typical features of the failure of the composite breakwaters. Therefore, understanding the motion response characteristics of caisson structures under wave action is of great importance for the design and the safe operation of caisson breakwaters. The dynamic response of caisson breakwaters under wave action is very complex, due to the interaction between wave-porous media-solid structures. In order to predict the stability of caisson breakwaters numerically, the complex free surface flow and the porous flow in the permeable foundation, as well as the contact interaction between the permeable foundation and the caisson structure should be accurately described. The existing numerical research for wave interaction with caisson breakwaters is usually assumed that the caisson structure is fixed in space, and the main interests focus on the wave deformation, the wave load acting on the caisson structure as well as the velocity and pressure fields in the vicinity of the composite breakwater. Few studies pay attention to the motion response and the instability of caisson structures. In addition, the traditional grid-based numerical models are commonly introduced to model wave interaction with the composite caisson breakwaters. These models, although powerful, may have difficulty dealing with extremely large deformation problems and usually also require an explicit surface capturing scheme. In comparison, the mesh-free smoothed particle hydrodynamics(SPH) method does not require the explicit surface capturing scheme in treating strong nonlinear flows with large free surface deformation and enables the easy modeling of coastal structures with complex geometrical boundaries. In this paper, based on the previously established SPH porous flow model, a contact interface boundary condition is developed between the permeable foundation and the upper caisson structure by modeling the supporting force and the sliding friction force at the interface boundary, and a new SPH model is established to study the caisson stability on the permeable foundation under wave action. Compared with the corresponding experimental data, it is found that the developed SPH model can reasonably predict the horizontal wave load, the vertical lift force acting on the caisson structure, and the motion response of the caisson structure. Compared with the other numerical model, it is found that the motion responses of the caisson structure predicted by the present SPH model have a better agreement with the experimental data. All the results indicate that the developed SPH model can be used as a robust tool to predict the stability of caisson breakwaters. However, it is undeniable that the predicted motion response of the caisson structure still deviates from the corresponding experimental data slightly. The main reason is that the contact interface boundary condition between the caisson structure and the permeable foundation ignores the deformation of the contact surface and the adjustment of the stress distribution, which is caused by the embedded effect of the caisson toe and the stone dislocation of the rubble-mound foundation.

Experimental and SPH studies of reciprocal wet-bed dam-break flow over obstacles

Different permutations of the single and the two-fold dam-break flow have been investigated using the mesh-free smoothed-particle hydrodynamics and the experimental setup. The free-surface deformation in the case with the wet bed for five different downstream water heights has been investigated and respective numerical and experimental results were presented. The results demonstrate that the increase of the water height over the wet bed leads to the reduction of the flow front velocity. Effect of considering or omitting the dam gate during the numerical simulation has also been examined, which proves that the simulations including the dam gate show improved agreement with the experimental results. Influence of the three-dimensional cubic, triangular, circular and square cylindrical obstacles and their position on flow characteristics has been investigated. As the distance between the triangular obstacle and the gate increases, a bore is created at the position closer to the top of the triangle. In addition, it is found that larger force is exerted on the circular cylinder in comparison to the square cylinder.

Smoothed particle hydrodynamic modelling of the cerebrospinal fluid for brain biomechanics: Accuracy and stability.

The Cerebrospinal Fluid (CSF) can undergo shear deformations under head motions. Finite Element (FE) models, which are commonly used to simulate biomechanics of the brain, including traumatic brain injury, employ solid elements to represent the CSF. However, the limited number of elements paired with shear deformations in CSF can decrease the accuracy of their predictions. Large deformation problems can be accurately modelled using the mesh‐free Smoothed Particle Hydrodynamics (SPH) method, but there is limited previous work on using this method for modelling the CSF. Here we explored the stability and accuracy of key modelling parameters of an SPH model of the CSF when predicting relative brain/skull displacements in a simulation of an in vivo mild head impact in human. The Moving Least Squares (MLS) SPH formulation and Ogden rubber material model were found to be the most accurate and stable. The strain and strain rate in the brain differed across the SPH and FE models of CSF. The FE mesh anchored the gyri, preventing them from experiencing the level of strains seen in the in vivo brain experiments and predicted by the SPH model. Additionally, SPH showed higher levels of strains in the sulci compared to the FE model. However, tensile instability was found to be a key challenge of the SPH method, which needs to be addressed in future. Our study provides a detailed investigation of the use of SPH and shows its potential for improving the accuracy of computational models of brain biomechanics.

Embedded smoothed particle hydrodynamics

In this paper, a hybrid method for embedding a meshfree smoothed particle hydrodynamics into mesh-based ALE hydro schemes is presented. The method relies on the embedded mesh framework presented in Puso et al. (2015, 2012) and utilizes SPH (Owen, 2010) in the solid foreground; when an appropriate damage or failure model is used with SPH, it becomes a natural way to model material fracture and cracking in high-explosive driven experiments. We provide various examples which validate the coupling between SPH and the embedded mesh method.

Modeling glass cooling mechanism with down-flowing water film via the smoothed particle hydrodynamics

This paper presents a new attempt to investigate the cooling mechanism of glass panes with down-flowing water film during fire outbreak by simulating the heat energy conservation equation using smoothed particle hydrodynamics (SPH) method. The nature of meshfree SPH method used allows us to predict the temperature distribution efficiently in continuous flow problems in contrast with mesh-based methods. To validate and show the efficiency of the proposed SPH model, the results from our simulation at specific conditions were compared with experimental measurements and results from commercial software packages. Furthermore, the new SPH model is utilized to simulate the effects of heat flux variation, down-flowing velocity and thickness of water film on temperature distribution of glass during fire. The developed SPH model is well able to describe glass cooling under different conditions. The computational results show that the rate of cooling increases when velocity or thickness of down-flowing water film increases. However, the glass temperature increases when heat flux increases.

Modelling 3D desiccation cracking in clayey soils using a size-dependent SPH computational approach

Modelling desiccation cracking in soils is a challenging process that requires a robust computational approach capable of describing soils undergoing thermo-hydro-mechanical coupling processes induced complex cracking patterns. To facilitate this process, this paper presents a computational approach that combines the mesh-free smoothed particle hydrodynamics (SPH) method and a size-dependent constitutive model with an embedded cohesive fracture process zone to simulate shrinkage induced soil cracking. The proposed method describes the fracture geometry through a set of SPH particles that carries their own cohesive fracture process zone and freely moves without being confined to a grid system. As it is a particle-based approach, there are no preferred orientations for cracks to develop, and hence the direction of crack propagation is controlled by local stress conditions and material properties only. This unique feature of SPH in conjunction with the size-dependent constitutive model enables the proposed method to naturally capture the crack propagation in soils while eliminating issues associated with spatial-dependent solutions. The proposed computational framework is verified against analytical solutions followed by the validation against experiment data of direct shear tests, flexural tests and shrinkage-induced soil cracking tests. Very satisfactory agreements with experimental data demonstrate that the proposed computational method is a promising approach for further incorporating multi-physical processes that can provide insights into the crack development processes in clayey soils.

Smoothed particle hydrodynamics simulation: a tool for accurate characterization of microfluidic devices

This work presents a two-dimensional (2D) model employing the mesh-free smoothed particle hydrodynamics (SPH) method for accurate characterization of microdevices. The simulator was validated by comparing analytical and numerical results from literature with the cases of Poiseuille, Couette, and biphase flow in microfluidic devices. Finally, a test case using two immiscible fluids in a cross-like device with three inputs and one output was computed. This device produces droplets in a flow-focusing configuration. The simulations produced similar flows when compared with theoretical, numerical, and experimental data reported in literature. When handling two liquid phases, such as water and oil, properties such as surface tension must be taken into account. These properties can be well modeled using the continuum surface force method, commonly applied for modeling capillarity in microdevice and microliquid applications. Thus, the implementation of the SPH method demonstrated that it represents a novel and promising alternative for simulation of emulsion formation in microfluidic devices.

Numerical simulations of oil flow inside a gearbox by Smoothed Particle Hydrodynamics (SPH) method

Abstract In this paper, numerical simulations of oil flow inside a gearbox are presented and compared to experimental particle image velocimetry (PIV) results. Instead of a traditional grid-based finite volume method, a mesh-free Smoothed Particle Hydrodynamics (SPH) method is employed. A multi-phase SPH formulation is utilized to resolve the complex multiphase fluid flow. A total of nine simulations are carried out for three oil levels and three Reynolds numbers, to investigate the flow field behavior and to compare with the experimental results. The aeration effect is first considered to qualitatively analyze the quantity and size of bubbles generated due to the rotation of the gears. Furthermore, the velocity field and velocity profile beneath the oil surface are comprehensively analyzed. Our simulation results exhibit physically consistent behavior of the oil flow and good agreement is achieved compared to the experimental results. Flow structures, splashing and recirculation areas are very well captured by the simulation. However, some discrepancies of the velocity field between the numerical and experimental results are also observed, and discussed.

Prediction of air blast mitigation in an array of rigid obstacles using smoothed particle hydrodynamics

The mitigation of blast waves propagating in air and interacting with rigid barriers and obstacles is numerically investigated using the mesh-free smoothed particle hydrodynamics method. A novel virtual boundary particle procedure with a skewed gradient wall boundary treatment is applied at the interfaces between air and rigid bodies. This procedure is validated with closed-form solutions for strong and weak shock reflection from rigid surfaces, supersonic flows over a wedge, formation of reflected, transverse, and Mach stem shocks, and also earlier experiments on interaction of a blast wave with concrete blocks. The mitigation of the overpressure and impulse transmitted to the protected structure due to an array of rigid obstacles of different shapes placed in the path of the blast wave is thereafter determined and discussed in the context of the existing experimental and numerical studies. It is shown that blockages having the shape of a right facing triangle or square placed in tandem or staggered provide better mitigation. The influence of the distance between the blockage array and protected structure is assessed, and the incorporation of a gap in the blockages is shown to improve the mitigation. The mechanisms responsible for the attenuation of air blast are identified through the simulations.

Three‐dimensional remeshed smoothed particle hydrodynamics for the simulation of isotropic turbulence

SummaryWe present a remeshed particle‐mesh method for the simulation of three‐dimensional compressible turbulent flow. The method is related to the meshfree smoothed particle hydrodynamics method, but the present method introduces a mesh for efficient calculation of the pressure gradient, and laminar and turbulent diffusion. In addition, the mesh is used to remesh (reorganise uniformly) the particles to ensure a regular particle distribution and convergence of the method. The accuracy of the presented methodology is tested for a number of benchmark problems involving two‐ and three‐dimensional Taylor‐Green flow, thin double shear layer, and three‐dimensional isotropic turbulence. Two models were implemented, direct numerical simulations, and Smagorinsky model. Taking advantage of the Lagrangian advection, and the finite difference efficiency, the method is capable of providing quality simulations while maintaining its robustness and versatility.

SPH MODELING OF VORTICITY GENERATION BY SHORT-CRESTED WAVE BREAKING

This study investigates vorticity generation by short-crested wave breaking by using the mesh-free Smoothed Particle Hydrodynamics model, GPUSPH. The short-crested waves are created by generating intersecting wave trains in a numerical wave basin with a beach. The capability of GPUSPH to simulate short-crested waves is first validated by laboratory measurements. Then we examine short-crested wave breaking with two incident wave heights H = 0.2 m and 0.3 m. The larger incident wave breaks at the toe of the planar beach, while the smaller incident wave breaks above the planar beach. The breaking wave profile, current field, nearshore circulation pattern, and vertical vorticity field due to short-crested wave breaking are carefully compared between two incident waves.

A coupled fluid-solid SPH approach to modelling flow through deformable porous media

In this paper, a computational framework based on the mesh-free smoothed particle hydrodynamics (SPH) method is developed to study the coupled behaviour of fluid and solid in a deformable porous medium. The mathematical framework developed herein is derived from the Biot's two-phase mixture theory in which the solid is modelled as an elasto-plastic material and the pore-fluid as an incompressible fluid. The key feature of the proposed numerical framework is that both solid and fluid phases are solved simultaneously in two different Lagrangian discretisations (or two different sets of Lagrangian particles) using their own governing equations that are linked through several laws of physics. The capability of the SPH method to model large deformation of the solid materials enables the framework to account for the permeability change due to the dilatant shear behaviour of the solid phase. To obtain a stable and accurate SPH solution for the pore-fluid, an incompressible SPH (ISPH) approach is adapted to correctly simulate the pore-pressure distribution of the fluid phase inside the porous medium. The proposed coupled SPH framework is firstly validated against analytical and solutions obtained using finite element method (FEM) for a submerged soil medium subjected to a gravitational load and a seepage flow through an elastic embankment, respectively. Then, it is employed for the simulation of flows through rockfill dams and an embankment failure induced by seepage flows. Simulation results predicted by SPH show very good agreements with analytical, FEM and experimental results. This suggests that the proposed two-phase SPH framework is a promising approach for future studies of coupled problems that involve complex water free-surface/seepage flows and large deformation of soils which are difficult to be modelled using traditional FEM-based coupled two-phase flow models.