Smoothed Particle Hydrodynamics Framework Research Articles

Macroscopic pedestrian flow simulation using Smoothed Particle Hydrodynamics (SPH)

Macroscopic pedestrian models are theoretically simpler than microscopic models, and they can potentially be solved faster while producing reasonable predictions of crowd dynamics. Therefore, they can be very useful for applications such as large-scale simulation, real-time state estimation and crowd management. However, the numerical methods presently used to solve macroscopic pedestrian models, which are mostly grid-based, have some shortcomings that limit their applicability. More specifically, they usually include complex procedures for grid generation and remeshing, and they produce simulation results that may not be sufficiently accurate (for example, because of unclear boundaries between flow states). Smoothed Particle Hydrodynamics (SPH) constitutes an alternative numerical method that could potentially overcome these limitations. SPH is a meshfree method where a crowd is represented by a set of particles that possess material properties and move according to macroscopic laws. Relevant state variables at each particle are approximated using information about the material properties of the neighboring particles and a smoothing function. This paper puts forward for the first time a generic SPH framework for solving macroscopic pedestrian models; in addition, it demonstrates that an SPH-based simulation model can produce meaningful and accurate results by means of three case studies. The first case study shows that the proposed numerical method can approximate well the analytical solution of a simple macroscopic model applied to a queue-discharge scenario. The second case study demonstrates that the proposed numerical method can potentially reproduce density dispersion (a phenomenon observed in real crowds) more accurately than grid-based methods, due to its meshfree, Lagrangian, and particle-based nature. The third case study highlights the need to reformulate the acceleration equation of the basic macroscopic model in order to reproduce lane formation in bi-directional flows (also an observed phenomenon) using the proposed SPH framework, and this paper presents a solution to do so.

An Improved Support Domain Model of Smoothed Particle Hydrodynamics Method to Simulate Crack Propagation in Materials

Smoothed particle hydrodynamics (SPH) has its unique advantages in simulating large deformation. However, in its calculation, it is easy for some regional particles to break off. This paper puts forward the concept of virtual crack boundary to solve crack propagating problems in the framework of SPH. The parameters of virtual crack boundary are determined by the projection method of descending dimension, which improves the support domains of crack tip particles. Based on the principle of minimum strain energy density factor in fracture mechanics, the initiation and extended directions of cracks in materials are estimated. By simulating the generation and expansion of three modes of cracks in materials, the SPH calculation results of the three types of support domain forms are compared with the ABAQUS simulation results and experiment results. It indicates that the method of virtual crack boundary method is more stable than the one based on discontinuous medium. And it can generate more reasonable results than the method based on continuous medium. This paper proves the effectiveness of strain energy density factor based on fracture mechanics theory in searching the direction of crack expansion using SPH, and explores the application of new support domain model in SPH crack solution.

Generating virtual process maps of SLM using powder-scale SPH simulations

In selective laser melting (SLM), three-dimensional parts are build up from a metal powder bed by layer-wise melting with a laser. While SLM offers a high flexibility in geometrical design and material texture, the interplay of dozens of parameters is difficult to analyze experimentally. The current research focuses on numerical simulation to increase confidence in manufactured parts and to reduce the time to market. Using a smoothed particle hydrodynamics (SPH) implementation on GPU, the 3D melt pool dynamics in a single laser track can be simulated within less than 2 h with a reasonable spatial resolution of 3 $$\upmu $$m. This is an extreme speedup compared to concurrent CFD methods that have recently been applied to the same problem. Using a SPH implementation on GPU, the 3D melt pool dynamics in a single laser track can be simulated within less than an hour with a reasonable spatial resolution of 3 $$\upmu $$m. This is an extreme speedup compared to concurrent CFD methods that have recently been applied to the same problem. The computational efficiency allows to conduct parameter studies, which before were prohibitively expensive, to generate a virtual process. To make the simulations possible a curvature calculation technique was applied, which is novel in the field of SPH. Additionally the advantage of a direct description of the internal energy is outlined by comparing the approach with the commonly applied apparent heat approach. Designers may profit from the fast simulations in two different scenarios: firstly, through a direct numerical simulation of certain parameter combinations and scenarios and, secondly, by informing advanced surrogate models or part-scale models to predict the behavior of the entire part being produced. When adapting the heat source model, the SPH framework may also be used to describe the related electron beam melting process.

A smoothed particle hydrodynamics (SPH) formulation of a two-phase mixture model and its application to turbulent sediment transport

A Smoothed Particle Hydrodynamics (SPH) formulation and implementation of the classical two-phase mixture model are reported, with a particular focus on the turbulent sediment transport and the sediment disturbances generated by moving equipment operating near or on the seabed. In the mixture model, the fluid-particle system is considered to be an equivalent medium whose evolution is described by a set of equations for the mixture continuity and momentum conservation, with the particle volume fraction being tracked by a transport equation. The governing equations are adapted to a Lagrangian, weakly-compressible SPH framework, the turbulence is modeled by a Reynolds-averaged Navier-Stokes approach, and adaptive boundary conditions for shear stress and turbulent quantities are implemented to account for laminar or turbulent local flow conditions. The complex rheological behavior of clay sediment/water mixtures is modeled using a volume fraction, shear rate-dependent viscosity which accounts for the existence of a yield stress. Hence, the proposed work encompasses several challenging modeling aspects: turbulence, non-Newtonian fluid behavior, sediment transport, and fluid-structure interactions. It is then illustrated on diverse cases of interest: a fluid-particle mixture column release, its subsequent turbulent transport and return to a hydrostatic equilibrium, the settling of particle clouds and two cases of particle-driven gravity currents, and their comparisons with available results. Finally, SPH simulation results for the disturbance of a bed of clay sediment/water mixture induced by a moving plate are reported and compared with experiments performed in our laboratory. The proposed SPH two-phase mixture model agrees well with the existing results considered in this study.

A multiphase SPH framework for supercooled large droplets dynamics

Purpose This paper aims to introduce a three-dimensional smoothed particle hydrodynamics (SPH) framework for simulating supercooled large droplets (SLD) dynamics at aeronautical speeds. Design/methodology/approach To include the effects of the surrounding air, a multiphase model capable of handling high density-ratio problems is adopted. A diffusive term is incorporated to smooth the density field and avoid numerical instabilities. Additionally, a particle shifting technique is used to eliminate anisotropic particle distributions. Findings The framework is validated against low-speed droplet impingement experimental results and then applied to the droplet impingement at high speeds typical of SLD conditions. Preliminary parametric studies are conducted to investigate the post-impact splashing. It is observed that a thicker water film can decrease the crown diameter and a smaller impact angle can suppress upward and forward splashing. Originality/value A three-dimensional multiphase SPH framework for SLD dynamics at a wide range of impact speed is developed and validated. The effects of particle resolution, water film thickness and impact angle on the post-impact crown evolution are investigated.

Smooth particle hydrodynamics studies of wet granular column collapses

Dry granular materials have been the subject of many investigations, while wet granular materials, which widely exist in many real-world applications, have only received limited attention. The aim of this paper is to address the missing gap in continuum modeling of wet granular materials. To study the wet granular flows, a grain-scale capillary interaction is introduced, as additional cohesive stress in the continuum-scale framework. We coupled the viscoplastic constitutive law for dry granular material and cohesion model for wet isotropic granular material to capture the behavior of wet granular materials. This combined model is implemented in a smooth particle hydrodynamics framework because the meshfree nature of this method captures the large deformation of granular flows without local grid distortion. The Wendland kernel is used as the interpolation kernel to improve numerical stability. This framework is validated by comparing numerical results with recent experimental findings for both dry and wet cases. The comparisons are illustrative of the potential of the framework to capture the behavior of granular materials across different phases. For different levels of friction and water content, the run-out dynamics and shear strength properties of granular materials in the final quasi-static regime are investigated. For granular flows on flat surfaces, compared with dry granular materials, with the introduction of surface tension in wet granular materials, it is found that there are increases in shear stresses locally and globally, enabling stronger internal forces to support structures with larger angles of repose. The surface energy-induced cohesion is found to play an important role in low friction cases compared to high friction cases. To benchmark the numerical framework presented here, granular column collapses on curved surfaces are also investigated. For flows on curved surfaces, although there are also increases in internal shear stresses, the differences in final profiles between wet granular materials and dry granular materials are not as pronounced as that on flat surfaces due to geometric constraints. The findings of this work are demonstrative of the capabilities of the smooth particle hydrodynamics method for the study of wet granular materials. This effort can serve as a step forward in the quest for a unified continuum theory and computational framework of granular material dynamics.

Smoothed particle hydrodynamics (SPH) for modeling fluid-structure interactions

Fluid-structure interaction (FSI) is a class of mechanics-related problems with mutual dependence between the fluid and structure parts and it is observable nearly everywhere, in natural phenomena to many engineering systems. The primary challenges in developing numerical models with conventional grid-based methods are the inherent nonlinearity and time-dependent nature of FSI, together with possible large deformations and moving interfaces. Smoothed particle hydrodynamics (SPH) method is a truly Lagrangian and meshfree particle method that conveniently treats large deformations and naturally captures rapidly moving interfaces and free surfaces. Since its invention, the SPH method has been widely applied to study different problems in engineering and sciences, including FSI problems. This article presents a review of the recent developments in SPH based modeling techniques for solving FSI-related problems. The basic concepts of SPH along with conventional and higher order particle approximation schemes are first introduced. Then, the implementation of FSI in a pure SPH framework and the hybrid approaches of SPH with other grid-based or particle-based methods are discussed. The SPH models of FSI problems with rigid, elastic and flexible structures, with granular materials, and with extremely intensive loadings are demonstrated. Some discussions on several key techniques in SPH including the balance of accuracy, stability and efficiency, the treatment of material interface, the coupling of SPH with other methods, and the particle regularization and adaptive particle resolution are provided as concluding marks.

Tracking of material orientation in updated Lagrangian SPH

This contribution demonstrates a continuum-mechanics-based method which yields the possibility of material orientation tracking within the smoothed particle hydrodynamics framework. The functionality provides the information on local orientation of particles, which is necessary for anisotropic material models, e.g., the kinematic hardening rule proposed by Prager. Such a model is expected to provide a possibility of a more precise simulation of complex industrial processes such as friction stir welding with three-dimensional material flow. The derivation of the method is presented for the updated Lagrangian formulation, in which the increment of the quaternion for the material point can be extracted from the gradient of velocity, following the continuum mechanics description. The examples of different complexity are demonstrated in order to verify the method: the rotating cylinder, torsion test, and industrial turning process. Additionally, the importance of kernel gradient correction adoption in order to preserve angular momentum in the presence of rotations is showcased.

Smoothed particle hydrodynamics (SPH) modeling of fiber orientation in a 3D printing process

We present a numerical study of the fused deposition modeling 3D printing process of fiber-reinforced polymers by means of Smoothed Particle Hydrodynamics (SPH). For this purpose, a classical microstructure-based fiber suspension model coupled with a constitutive model for the suspending polymer is implemented within an SPH framework. The chosen model is reviewed, together with the details and specificities of its implementation in SPH. The results for several representative cases are then presented, mainly in terms of contours of fiber orientation tensor components and orientation distributions across the deposited layer thickness. The impact of the fiber concentration and its aspect ratio in a semi-concentrated regime and the effect of the ratio between extrusion and substrate velocities are investigated. Some insights into the link between the flow field and fiber orientation evolution within the printing head and as the material exits the nozzle are given. The main findings lie in the prediction of a skin/core structure in the deposited layer in which the skin regions exhibit a higher fiber alignment with respect to the core region. This effect is found to be enhanced by an increase in fiber concentration and to be sensitive to the substrate-to-extrusion velocity ratio. It is indeed enhanced in cases where the substrate velocity is low compared to the extrusion velocity and accompanied by a larger swelling of the deposit at the nozzle exit.

On consistency and energy conservation in smoothed particle hydrodynamics

SummaryEnergy conservation and consistency are not easy to achieve simultaneously in smoothed particle hydrodynamics (SPH). In this study, an efficient strategy is proposed to achieve energy conservation in an SPH framework with a consistent basis function. Herein, at every particle pair interaction, a correction term is introduced such that energy conservation is restored locally and, at the same time, the total variation of different variables due to the correction term is minimum. The final form of the proposed formulation is such that no additional computational effort is required and the simplicity of SPH is preserved. The theoretical error estimate of the proposed formulation is performed. The proposed scheme is also compared with benchmark SPH formulations in terms of the L2 error norm for representative functional derivatives both in regular and irregular particle distributions. Finally, the efficacy of the proposed formulation in conserving energy and maintaining accuracy is demonstrated via few elastic, elastic‐plastic impact and fracture problems.

A mixed characteristic boundary condition for simulating viscous incompressible fluid flows around a hydrofoil

Smoothed particle hydrodynamics (SPH) is a meshfree method and has been widely used in the field of fluid dynamics. However, there is still a lack of robust approach to implement the far-field boundary condition in the simulation of free stream flow past the rigid body. To solve this problem, on the basis of Lastiwka et al.’s work, an improved non-reflecting boundary condition, called mixed characteristic boundary condition is proposed in this paper. The mixed characteristic boundary condition is tested by two-dimensional incompressible flows with a perturbation at the initial moment. The numerical results show that the mixed characteristic boundary condition can effectively suppress the reflection of waves on far-field boundaries. Finally, flows past a hydrofoil are simulated within the framework of the kernel gradient free SPH in two kinds of non-reflecting boundary condition. The results indicate that the present boundary condition is more robust and suitable for SPH than the one adopted by Lastiwka et al.

SPH modeling of fluid-structure interaction

This work concerns numerical modeling of fluid-structure interaction (FSI) problems in a uniform smoothed particle hydrodynamics (SPH) framework. It combines a transport-velocity SPH scheme, advancing fluid motions, with a total Lagrangian SPH formulation dealing with the structure deformations. Since both fluid and solid governing equations are solved in SPH framework, while coupling becomes straightforward, the momentum conservation of the FSI system is satisfied strictly. A well-known FSI benchmark test case has been performed to validate the modeling and to demonstrate its potential.

A smoothed particle hydrodynamics framework for modelling multiphase interactions at meso-scale

A smoothed particle hydrodynamics (SPH) framework is developed for modelling multiphase interactions at meso-scale, including the liquid–solid interaction induced deformation of the solid phase. With an inter-particle force formulation that mimics the inter-atomic force in molecular dynamics, the proposed framework includes the long-range attractions between particles, and more importantly, the short-range repulsive forces to avoid particle clustering and instability problems. Three-dimensional numerical studies have been conducted to demonstrate the capabilities of the proposed framework to quantitatively replicate the surface tension of water, to model the interactions between immiscible liquids and solid, and more importantly, to simultaneously model the deformation of solid and liquid induced by the multiphase interaction. By varying inter-particle potential magnitude, the proposed SPH framework has successfully simulated various wetting properties ranging from hydrophobic to hydrophilic surfaces. The simulation results demonstrate the potential of the proposed framework to genuinely study complex multiphase interactions in wet granular media.

A purely Lagrangian method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics

It has long been suggested that a purely Lagrangian solution to global-scale atmospheric/oceanic flows can potentially outperform tradition Eulerian schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully Lagrangian method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed.

Smoothed Particle Hydrodynamics for investigating hydraulic and mechanical behaviour of an embankment under action of flooding and overburden loads

Extreme weather events, such as floods, are becoming more frequent in future with all consequences concerning the safety especially of water retaining structures, in particular, levees used as technical flood protection. The knowledge and correct consideration of coupled hydro-mechanical processes influencing the failure and post-failure behaviour of water saturated soils are of paramount significance for the assessment of hydraulically loaded geotechnical structures. This study focuses on the modelling of the processes governing the behaviour of water saturated soils using Smoothed Particle Hydrodynamics (SPH) on the example of a homogeneous embankment under different loading conditions. This paper aims to improve available SPH framework in order to enhance soil-water interaction in this method for geotechnical engineering investigations. To achieve this goal, the suggested approach is validated intensively by various well-known problems. Finally, the verified tool is used to investigate the hydro-mechanical behaviour of homogeneous embankments under simultaneous hydraulic and mechanical loading. The simulation results prove that the suggested approach is capable of simulating relevant hydraulic and mechanical processes governing the deformation behaviour of hydraulically loaded structures beyond the failure point allowing the detailed analysis of the post-failure behaviour characterised by large deformations.

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.

Two-phase smooth particle hydrodynamics modeling of air-water interface in aerated flows

The large deformations associated with air and water interactions are critical factors that affect the hydrodynamic characteristics of hydraulic structures. As a type of Lagrange meshless particle method, smoothed particle hydrodynamics (SPH) has been shown to have many advantages when modeling the interface flow and tracing the free surface because the particles inherit the velocity, mass, and density properties. Significant theoretical and numerical studies have been performed recently in this area. In the present study, a two-phase SPH framework was developed based on these previous studies and we explored its capacity to capture the main features of large density ratio aerated flows. The cohesive pressure was included only in the momentum equation of the air phase for additional amendments to ensure the stability and accuracy of the two-phase SPH model. Three case studies were performed to test the performance of the two-phase SPH model. A convergence study demonstrated the need to balance the CPU time consumption and the real-time requirements. A dam-break simulation based on pressure variation in the air pocket showed the superior analytical performance of the two-phase model compared with the single-phase model. The results of a hydraulic jump simulation were compared with the theoretical results in order to understand the collision between the solid and liquid using the SPH method more clearly. Thus, the consistency between the simulation and the theoretical and experimental results demonstrated the feasibility and stability of the two-phase SPH framework.

Computational Studies on Interactions between Robot Leg and Deformable Terrain

Dynamic interactions with soft terrain occur in many natural and engineering systems. These events are usually associated with large deformations and plastic flows, which generate unique challenges for grid-based techniques because of local grid distortions. To overcome this issue, the application of Smooth Particle Hydrodynamics (SPH) method is first extended by the authors to the field of terradynamics, in particular, the continuum simulation of legged locomotion on soft soil media. Soil models with and without consideration of plastic failure are introduced to capture the behavior of loose and dense soil terrain. In one of the models considered for legged locomotion, a pendulum model is used to study a swinging mode. Locomotive interactions across different frequencies are introduced to realize quasi-static deformations and rapid collisional flow phenomena. The results obtained from numerical studies reveal that the soil behavior during locomotive interactions can be realistically simulated with the SPH framework. Compared with a dense soil terrain, a loose soil terrain has better characteristics of energy storage and dissipation. These findings can be helpful for understanding possibilities for robot navigation and exploration in unknown and complex terrains.

Development of stress boundary conditions in smoothed particle hydrodynamics (SPH) for the modeling of solids deformation

This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.

Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach.

Biological soft tissues experience damage and failure as a result of injury, disease, or simply age; examples include torn ligaments and arterial dissections. Given the complexity of tissue geometry and material behavior, computational models are often essential for studying both damage and failure. Yet, because of the need to account for discontinuous phenomena such as crazing, tearing, and rupturing, continuum methods are limited. Therefore, we model soft tissue damage and failure using a particle/continuum approach. Specifically, we combine continuum damage theory with Smoothed Particle Hydrodynamics (SPH). Because SPH is a meshless particle method, and particle connectivity is determined solely through a neighbor list, discontinuities can be readily modeled by modifying this list. We show, for the first time, that an anisotropic hyperelastic constitutive model commonly employed for modeling soft tissue can be conveniently implemented within a SPH framework and that SPH results show excellent agreement with analytical solutions for uniaxial and biaxial extension as well as finite element solutions for clamped uniaxial extension in 2D and 3D. We further develop a simple algorithm that automatically detects damaged particles and disconnects the spatial domain along rupture lines in 2D and rupture surfaces in 3D. We demonstrate the utility of this approach by simulating damage and failure under clamped uniaxial extension and in a peeling experiment of virtual soft tissue samples. In conclusion, SPH in combination with continuum damage theory may provide an accurate and efficient framework for modeling damage and failure in soft tissues.