Smoothed Particle Hydrodynamics Framework Research Articles

Numerical simulation of wedges slamming non-Newtonian fluids based on SPH method

Current research on non-Newtonian fluids using Smoothed Particle Hydrodynamics (SPH) has primarily focused on dynamic behavior, with limited exploration into interactions between rigid bodies and non-Newtonian fluids. Leveraging the SPH method's effectiveness in addressing free surface flow challenges, a two-dimensional numerical model of a rigid body impacting non-Newtonian fluids based on the Herschel-Bulkley-Papanastasiou (HBP) constitutive model is developed within the SPH framework. The study integrates experimental and numerical findings from non-Newtonian dam break scenarios, comparing particle distribution and the evolution of the waterfront over time to ensure accurate representation of non-Newtonian fluid behavior. While ensuring the convergence of SPH results, the research simulates the impact of a wedge on the surface of non-Newtonian fluids. This comparison of the slamming load exerted by non-Newtonian fluids on the wedge serves to validate the accuracy of the numerical method. Furthermore, the study explores the effects of varying initial velocities and roll angles of wedges slamming into specific non-Newtonian fluids. It analyzes fluid jet phenomena and changes in slamming loads.

Smoothed particle hydrodynamics implementation of the standard viscous–plastic sea-ice model and validation in simple idealized experiments

Abstract. The viscous–plastic (VP) rheology with an elliptical yield curve and normal flow rule is implemented in a Lagrangian modelling framework using the smoothed particle hydrodynamics (SPH) meshfree method. Results show, from a perturbation analysis of SPH sea-ice dynamic equations, that the classical SPH particle density formulation expressed as a function of sea-ice concentration and mean ice thickness leads to incorrect plastic wave speed. We propose a new formulation for particle density that gives a plastic wave speed in line with theory. In all cases, the plastic wave in the SPH framework is dispersive and depends on the smoothing length (i.e., the spatial resolution) and on the SPH kernel employed in contrast to its finite-difference method (FDM) implementation counterpart. The steady-state solution for the simple 1D ridging experiment is in agreement with the analytical solution within an error of 1 %. SPH is also able to simulate a stable upstream ice arch in an idealized domain representing the Nares Strait in a low-wind regime (5.3 m s−1) with an ellipse aspect ratio of 2, an average thickness of 1 m and free-slip boundary conditions in opposition to the FDM implementation that requires higher shear strength to simulate it. In higher-wind regimes (7.5 m s−1) no stable ice arches are simulated – unless the thickness is increased – and the ice arch formation showed no dependence on the size of particles, in contrast to what is observed in the discrete-element framework. Finally, the SPH framework is explicit, can take full advantage of parallel processing capabilities and shows potential for pan-Arctic climate simulations.

A modified SPH framework of for simulating progressive rock damage and water inrush disasters in tunnel constructions

To date, numerically simulating the Fluid–Solid Interaction (FSI) and the entire process of host rock damage and water inrush involved in tunnel construction relies intensively on hybrid methods of two or more numerical codes, which commonly encounter deficiency in learning, modelling and computation. A modified framework of Smoothed Particle Hydrodynamics (SPH), the Coupled Discontinuous SPH (CDSPH) method, was developed to simulate cracking, contacting and large deformation of rock blocks, free surface flow and the FSI for water/mud inrush disasters in tunnel construction through water–rich stratums. The failed SPH particles were transformed to discontinuous particles and new contacts between these particles were formed to simulate the frictional slip and separation/compression between fracture walls. The improved SPH method was employed to a water inrush case of a tunnel and the simulation results indicate that the entire process of progressive rock damage, water inrush and flooding are precisely reproduced by the improved method. The greater kinematic viscosity of fluids and rock wall thickness can increase the flow velocity and hence increasing the impact pressure of floods, and the failure pattern of the rock wall changes from partial outburst to complete failure. Vulnerability analysis of the water inrush reveals a complete damage status for people, vehicles and Non-RC frame buildings, and a moderate to complete damage to RC frame buildings at the tunnel portal. This single code is capable of simulating the behaviour of rocks, fluids and their interactions in catastrophic disasters that is potentially applicable to a wide spectrum of surface and subsurface problems involving FSI.

Numerical studies of complex fluid-solid interactions with a six degrees of freedom quaternion-based solver in the SPH framework

Six-degree-of-freedom (6-DOF) motions of structures widely exist in aeronautics and ocean engineering. It is significant to study the 6-DOF motion for simulating the trajectory and impact load of structures. This paper uses the smoothed particle hydrodynamics (SPH) method combined with some modified numerical techniques to simulate the fluid-solid interactions (FSI), then a quaternion-based method is adopted to simulate the free motion of rigid bodies, where the calculation process of 6-DOF motions based on quaternion is elaborated in detail. The accuracy of this method is verified through two benchmark tests, including water entry of a cuboid and skipping stone, which can prove the pressure calculation and motion prediction of rigid bodies are consistent with the experimental results. At last, the 6-DOF ditching process of a seaplane is simulated by the quaternion method embedded in the SPH model, and the simulation results are consistent with those simulated by the finite volume method (FVM). The above three tests demonstrate that the SPH model combined with a 6-DOF quaternion-based solver can accurately solve FSI problems from basic to complex at different scales. Besides, the SPH model shows significant advantages in capturing large-deformed free surfaces and splashing droplets compared with Eulerian-grid-based methods.

A class of second-derivatives in the Smoothed Particle Hydrodynamics with 2nd-order accuracy and its application to incompressible flow simulations

In this paper, we propose a class of decoupled first- and second-derivatives models for the Smoothed Particle Hydrodynamics (SPH) method, which were inspired by the Lagrangian Differencing Dynamics (LDD) (Bašić et al., 2018) and (Bašić et al., 2022) and arranged to the SPH framework. Being extensions of existing gradient and Laplacian SPH models, the proposed decoupled models include the cross-derivatives, which are crucial to ensure 2nd-order accuracy. Under the framework of the proposed class of decoupled models, we defined five second-derivative models, here termed, Naïve (NI), Block Diagonal (BD), SUM, Part Inverse (PI), and Full Inverse (FI). Among these models, only the NI and BD have equivalences in existing models, while the other three are completely original. Therefore, we believe that, besides the development of new models, this work may provide a standard classification for second-derivative models in SPH. In addition, applying the FI model into the first-derivative model, we propose the first instance of a 2nd-order accurate gradient model in SPH.Then, we demonstrated that the convergence rate of the truncation error decreases the higher the order of the model, and the results were investigated for different particle disorder levels. After that, we applied the proposed derivative models to incompressible fluid flow simulations for validation. The validation includes four famous benchmark tests: the lid-driven cavity, the Kármán vortex behind a cylinder, the rotating square patch, and the dam break problem. The first two tests are used to discuss the accuracy of the spatial derivative models without a free surface, while the third test already includes the effects of the free surface, where particle disorder is more severe. All examples demonstrate the robustness and accuracy of our proposed spatial derivatives at 2nd-order accuracy. Since the combination of the FI Laplacian model and the 2nd-order gradient model can satisfy 2nd-order accuracy, we expect this to be the second generation of SPH formulations, which we call SPH(2).

An Optimization‐based SPH Solver for Simulation of Hyperelastic Solids

AbstractThis paper proposes a novel method for simulating hyperelastic solids with Smoothed Particle Hydrodynamics (SPH). The proposed method extends the coverage of the state‐of‐the‐art elastic SPH solid method to include different types of hyperelastic materials, such as the Neo‐Hookean and the St. Venant‐Kirchoff models. To this end, we reformulate an implicit integration scheme for SPH elastic solids into an optimization problem and solve the problem using a general‐purpose quasi‐Newton method. Our experiments show that the Limited‐memory BFGS (L‐BFGS) algorithm can be employed to efficiently solve our optimization problem in the SPH framework and demonstrate its stable and efficient simulations for complex materials in the SPH framework. Thanks to the nature of our unified representation for both solids and fluids, the SPH formulation simplifies coupling between different materials and handling collisions.

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

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

Smoothed particle hydrodynamics method for free surface flow based on MPI parallel computing

In the field of computational fluid dynamics (CFD), smoothed particle hydrodynamics (SPH) is very suitable for simulating problems with large deformation, free surface flow and other types of flow scenarios. However, traditional smoothed particle hydrodynamics methods suffer from the problem of high computation complexity, which constrains their application in scenarios with accuracy requirements. DualSPHysics is an excellent smoothed particle hydrodynamics software proposed in academia. Based on this tool, this paper presents a largescale parallel smoothed particle hydrodynamics framework: parallelDualSPHysics, which can solve the simulation of large-scale free surface flow. First, an efficient domain decomposition algorithm is proposed. And the data structure of DualSPHysics in a parallel framework is reshaped. Secondly, we proposed a strategy of overlapping computation and communication to the parallel particle interaction and particle update module, which greatly improves the parallel efficiency of the smoothed particle hydrodynamics method. Finally, we also added the pre-processing and post-processing modules to enable parallelDualSPHysics to run in modern high performance computers. In addition, a thorough evaluation shows that the 3 to 120 million particles tested can still maintain more than 90% computing efficiency, which demonstrates that the parallel strategy can achieve superior parallel efficiency.

An Extended Hydro-Mechanical Coupling Model Based on Smoothed Particle Hydrodynamics for Simulating Crack Propagation in Rocks under Hydraulic and Compressive Loads

A seepage model based on smoothed particle hydrodynamics (SPH) was developed for the seepage simulation of pore water in porous rock mass media. Then, the effectiveness of the seepage model was proved by a two-dimensional seepage benchmark example. Under the framework of SPH based on the total Lagrangian formula, an extended hydro-mechanical coupling model (EHM-TLF-SPH) was proposed to simulate the crack propagation and coalescence process of rock samples with prefabricated flaws under hydraulic and compressive loads. In the SPH program, the Lagrangian kernel was used to approximate the equations of motion of particles. Then, the influence of flaw water pressure on crack propagation and coalescence models of rock samples with single or two parallel prefabricated flaws was studied by two numerical examples. The simulation results agreed well with the test results, verifying the validity and accuracy of the EHM-TLF-SPH model. The results showed that with the increase in flaw water pressure, the crack initiation angle and stress of the wing crack decreased gradually. The crack initiation location of the wing crack moved to the prefabricated flaw tip, while the crack initiation location of the shear crack was far away from the prefabricated flaw tip. In addition, the influence of the permeability coefficient and flaw water pressure on the osmotic pressure was also investigated, which revealed the fracturing mechanism of hydraulic cracking engineering.

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics.

Smoothed particle hydrodynamics (SPH), as one of the earliest meshfree methods, has broad prospects in modeling a wide range of problems in engineering and science, including extremely large deformation problems such as explosion and high velocity impact. This paper aims to provide a comprehensive overview on the recent advances of SPH method in the fields of fluid, solid, and biomechanics. First, the theory of SPH is described, and improved algorithms of SPH with high accuracy are summarized, such as the finite particle method (FPM). Techniques used in SPH method for simulating fluid, solid and biomechanics problems are discussed. The δ-SPH method and Godunov SPH (GSPH) based on the Riemann model are described for handling instability issues in fluid dynamics. Next, the interface contact algorithm for fluid-structure interaction is also discussed. The common algorithms for improving the tensile instability and the framework of total Lagrangian SPH are examined for challenging tasks in solid mechanics. In terms of biomechanics, the governing equations and the coupling forces based on SPH method are exemplified. Then, various typical engineering applications and recent advances are elaborated. The application of fluid mainly depicts the interaction between fluid and rigid body as well as elastomer, while some complicated fluid-structure interaction ocean engineering problems are also presented. In the aspect of solid dynamics, galaxy, geotechnical mechanics, explosion and impact, and additive manufacturing are summarized. Furthermore, the recent advancements of SPH method in biomechanics, such as hemodynamically and gut health, are discussed in general. In addition, to overcome the limitations of computational efficiency and computational scale, the multiscale adaptive resolution, the parallel algorithm and the automated mesh generation are addressed. The development of SPH software in China and abroad is also summarized. Finally, the challenging task of SPH method in the future is summarized. In future research work, the establishment of multi-scale coupled SPH model and deep learning technology in solid and biodynamics will be the focus of expanding the engineering applications of SPH methods.

High-velocity impact study of an advanced ceramic using finite element model coupling with a machine learning approach

A numerical approach combining finite element modeling and machine learning is used to inform the material performance of an alumina ceramic tile undergoing high-velocity impact. In this study, the alumina ceramic tile is simulated by incorporating a user-defined Johnson–Holmquist–Beissel (JHB) material model within the framework of smoothed particle hydrodynamics (SPH) in LS-DYNA finite element software. The implementation of the JHB model is verified by comparing equivalent stress–pressure responses through a single element simulation test. After implementation, the computational framework is simulated across our chosen range of conditions by matching the results from both plate impact experiments and ballistic testing from the literature. The computational model is then used to generate training data sets for an artificial neural network (ANN) to predict the residual velocity and projectile erosion for an alumina ceramic tile undergoing high-velocity impact in the SPH framework. The ANN is then used to perform a sensitivity analysis involving exploring the effect of mechanical properties (e.g., strength and shear modulus) and impact simulation geometries (e.g., thickness of ceramic tile) on material performance (i.e., residual projectile velocity and erosion). Overall, this study shows the capability of the FEM-ANN approach in studying the high-velocity impact on ceramic tiles and is applicable to guide the structural-scale design of ceramic-based protection systems.

A novel MPI-based parallel smoothed particle hydrodynamics framework with dynamic load balancing for free surface flow

This paper presents a new Smoothed Particle Hydrodynamics (SPH) parallel framework, which is designed for free surface flows and is scalable on a High Performance Computer (HPC). The framework is accomplished by adopting a Message Passing Interface (MPI) approach with a domain partitioning strategy. A regular background grid is used to partition the entire computational domain and each subdomain is labelled using an index ordering method. Adjacent subdomains can be determined by the index list, and avoid global communications in the particle distribution process. Within the local grid, the grid is divided into an internal grid as well as an interactive grid to identify the particles for which information is to be transferred. The implementation of the dynamic loading balance strategy considers two different ways of determining loading: computation particle numbers and running time. The dynamic load balance strategy repositions neighbouring subdomains based on the local load imbalance between cores. To demonstrate the framework's capacity and distinctive properties, a variety of free surface flow benchmarks are studied. Intensive numerical experiments at various scales are used to assess the performance in detail.

Reversible inter-particle bonding in SPH for improved simulation of friction stir welding

Friction stir welding (FSW) is a complex joining process which is governed by multiple intertwined physical phenomena. Besides friction, inelastic heat generation, and heat conduction, it involves high plastic deformations, resulting in a need for a numerical method being able to handle all these. Such a scheme is smoothed particle hydrodynamics (SPH), which is a mesh-free computational technique. Absence of a fixed mesh results in the ability of the method to deal with another challenge of friction stir welding, a coalescence of initially separate workpieces into one due to bonding mechanisms. The background of this phenomenon is a transition from contact between two pieces to one continuum due to enormous changes in several material condition, such as temperature, pressure, strain, and strain rate. This work deals with a new development related to bonding, which will provide deeper understanding about the physical weld formation during FSW. The SPH framework must be extended to consider this bonding mechanism. This involves the bonding criterion definition, the interaction type change, and the SPH–SPH contact formulation. Then, the implementation is tested for two different examples, a compression test and FSW.

A computationally efficient SPH framework for unsaturated soils and its application to predicting the entire rainfall-induced slope failure process

The first and fully validated smoothed particle hydrodynamics (SPH) model is presented to tackle coupled flow–deformation problems in unsaturated porous media that undergo large deformation and post-failure behaviour. Unlike the commonly adopted double-layer SPH framework for saturated soils, this paper presents a three-phase single-layer SPH model capable of predicting anisotropic seepage flows through porous media and their complete time-dependent transition from unsaturated to saturated states, as well as their influence on the mechanical behaviour of the porous media and vice versa. The mathematical framework is developed based on Biot's mixture theory and discretised using the authors’ recently developed novel SPH approximation scheme for the second derivatives of a field quantity. The soil is modelled using a suction-dependent elastoplastic constitutive model, expressed in terms of effective stress and suction. In addition, an adaptive two-timescale scheme is proposed for the first time to address existing challenges in solving coupled-flow large-deformation problems that involve a significant difference in the timescale required for the solid and fluid phases. The capability of the proposed SPH model was demonstrated through fundamental consolidation tests and a large-scale rainfall-induced slope failure experiment. Very good agreements with theoretical solutions and experimental results are achieved, suggesting that the proposed SPH model can be readily extended to solve a wide range of large-scale geotechnical applications involving coupled unsaturated seepage–deformation problems.

An implicit SPH-based structure model for accurate Fluid–Structure Interaction simulations with hourglass control scheme

This work is dedicated to development of an implicit SPH (Smoothed Particle Hydrodynamics)-based structure model as well as its integrated purely Lagrangian meshfree hydroelastic FSI (Fluid–Structure Interaction) solver for consistent, accurate and stable modeling of FSI problems. The implicit structure model is established in the context of Hamiltonian mechanics under the assumption of linear elastic solid. Four refined schemes are introduced for improved accuracy, consistency, efficiency and stability: two formerly developed schemes, [i] HT (High-order implicit Time integration) scheme, [ii] HD (High-order Discretization) operator scheme; as well as the novel two schemes newly proposed in this work, namely [iii] IPC (Iterative Predictor–Corrector) calculation procedures to minimize errors related to an imprecise assumption on rotation matrix and [iv] IHC (Implicit Hourglass Control) scheme for stabilizing simulation by suppressing spurious zero-energy modes. An enhanced particle-based FSI solver is formulated within a unified SPH framework by integrating a refined ISPH (Incompressible SPH) fluid model and the proposed implicit structure model, which allows consistent fluid–structure time coupling adopting the equivalent time step sizes in both phases. The proposed implicit structure model and FSI solver are configured in two-dimensions and validated with several 2D structure and FSI benchmark tests showing that our proposed implicit framework could provide almost consistent robustness, accuracy and efficiency with respect to the explicit one.

The Effective Thermal Conductivity of Unsaturated Porous Media Deduced by Pore-Scale SPH Simulation

The smoothed particle hydrodynamics (SPH) method was employed to simulate the heat transfer process in porous media at the pore scale. The effective thermal conductivity of a porous medium can be predicted through a simulation experiment of SPH. The accuracy of the SPH simulation experiment was verified by comparing the predicted values with reference values for ideal homogeneous media and multiphase layered media. 3D simulation experiments were implemented in granular media generated by the PFC method. Based on the SPH framework, a concise method was proposed to produce unsaturated media by simulating the wetting process in dry media. This approach approximates the formation of liquid bridges and water films on granules. Through simulation experiments, the empirical formula of the variation in thermal conductivity with the degree of saturation was tested. The results showed that the reciprocal of the normalized thermal conductivity and the reciprocal of the saturation are linearly related, which is in line with the empirical formula proposed by Cote and Konrad.

A pseudo-spring based SPH framework for studying fatigue crack propagation

The existing smoothed particle hydrodynamics (SPH) approaches for propagating fatigue cracks involve either the deletion of the crack front particle or stopping all its interactions in the total Lagrangian form. Here, we adopt the pseudo-spring-based Eulerian form of SPH to model mode-I fatigue crack propagation. For modeling fatigue crack growth, only the interactions between the crack front particle and its neighbors, which display the largest axial stresses in the connected pseudo-springs, are stopped. We show that our framework can determine accurately the mode-I stress intensity factors (SIFs) and capture both the fatigue crack path and the fatigue life of different specimens.

An Effective Smoothing Length Updating Method for Smoothed Particle Hydrodynamics

Smoothing length plays a significant role in smoothed particle hydrodynamics (SPH). Inappropriate smoothing length will result in problems of stability, accuracy and efficiency. Updating smoothing length with time is very important for SPH modeling of large deformation problems. In this work, an effective smoothing length updating method is proposed. The method works in the framework of SPH with scalar smoothing length. It is quite simple in implementation and is computationally efficient. The method updates smoothing length according to maximum local particle spacing and inhomogeneity of material deformation. Numerical examples in both 2D and 3D which involve large deformation are calculated to validate the effectiveness of the proposed method. A comparison between the proposed method and several traditional methods is performed. Numerical results show that the present method can adapt to the simulation of severely inhomogeneous deformation and produce better stability and accuracy than the traditional methods for SPH modeling of large deformation problems.

A Smoothed Particle Hydrodynamics Framework for Interaction Between Ice and Flexible Pile

A Smoothed Particle Hydrodynamics Framework for Interaction Between Ice and Flexible Pile

A numerical study of a taut-moored point-absorber wave energy converter with a linear power take-off system under extreme wave conditions

Probably the biggest challenge for wave energy is to ensure survival in harsh offshore conditions, in order to reduce costs for offshore repair operations and downtime, and achieve economic viability. This work presents a reliable numerical tool that can be used to study the dynamics and survivability of wave energy converters in violent wave conditions, possibly cutting down the costs of experimental campaigns. Within the Smoothed Particle Hydrodynamics framework, this research identifies a detailed procedure to model a taut-moored point-absorber wave energy converter together with its inherent power take-off device, which seamlessly exploits its functions of energy harvesting and load bearing. A validation of the DualSPHysics code is provided by contrasting the numerical outcome with a thorough set of data obtained in physical tests with extreme waves, showing that the time-integrated numerical model can capture with good accuracy all the physics involved. The computational fluid dynamics tool is employed to perform a survivability study, modeling high-return period wave conditions for marine structures, and providing guidelines on how to create the numerically best setup to be used for design purposes. A real-like irregular sea state representation, comprising 500 waves, was used to draw insightful indications for the structure optimization to increase the structure’s life expectancy, or conversely, to reduce the initial and operational costs.