Smoothed Particle Hydrodynamics Approach Research Articles

Smoothed particle hydrodynamics approach for modelling submerged granular flows and the induced water wave generation

In this study, we develop a Smoothed Particle Hydrodynamics (SPH) 2D-model for simulating fully submerged granular flows and their arising water waves. The granular particles are characterised by a non-Newtonian flow pattern, following a Casson constitutive law, generalised by applying the infinitesimal strain theory to avoid numerical singularities inherited from the original law. The implementation of this rheological model on the weakly compressible viscous Navier-Stokes equations enables the simultaneous modelling of the motion of granular flows and their resulting water waves, establishing a monolithic representation of fluid-structure coupling. The novelty of this model lies in the numerical continuity of the generalised rheological model based mainly on the yield stress criterion, which is computed purely from the mechanical properties of granular materials, including internal friction, cohesion, and viscosity coefficients. The proposed SPH model is validated through two benchmarks available in the literature, representing a submarine landslide along an inclined plane and an immersed granular column collapse. The outcomes of our study illustrate the effectiveness of the proposed model in accurately predicting the motions of submerged granular masses and their resulting water waves, which is crucial for accurately predicting the behaviour of underwater landslides and other natural hazards.

3D numerical simulation and experimental validation of resin-bonded sand gravity casting: Filling, cooling, and solidification with SPH and ProCAST approaches

This article provides a comprehensive investigation into the resin-bonded sand gravity casting process, with a focus on the filling, cooling, and solidification steps. The research combines numerical simulations and experimental validation in a three-dimensional (3D) configuration, utilizing a realistic filling system. The study employs three approaches—experimental tests, Smoothed Particle Hydrodynamics (SPH) simulations, and ProCAST simulations—to analyze the filling, cooling, and solidification steps. Two different molds were used in the experiments. The first mold has a transparent glass component in front of the plate, enabling observation and recording of the filling process, while the second mold, used solely for thermal analysis, did not incorporate any glass component. The SPH approach yields more accurate results for the filling time, liquid level height, and morphology when compared to ProCAST. The discrepancy in final filling time for the desired casting part between the experiment and SPH is 5.13 %, and the difference between the experiment and ProCAST is 15.38 %. Additionally, the cooling and solidification steps are investigated through an analysis of cooling curves. The numerical methods demonstrate slightly higher cooling rates and deviations in solidification times compared to the experimental data, mainly due to the thermal Neumann boundary condition. Furthermore, the average discrepancy in solidification time for five points of the intended casting component between the experiment and SPH is 8.60 %, whereas when compared with ProCAST, the discrepancy increases to 9.13 %.

Implicit Surface Tension for SPH Fluid Simulation

The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force based approach for the simulation of surface tension effects using the Smoothed Particle Hydrodynamics (SPH) method. We define a continuous formulation inspired by the properties of surface tension at the molecular scale which is spatially discretized using SPH. An adapted variant of the linearized backward Euler method is used for time discretization, which we also strongly couple with an implicit viscosity model. Finally, we extend our formulation with adhesion forces for interfaces with rigid objects. Existing SPH approaches for surface tension in computer graphics are mostly based on explicit time integration, thereby lacking in stability for challenging settings. We compare our implicit surface tension method to these approaches and further evaluate our model on a wider variety of complex scenarios, showcasing its efficacy and versatility. Among others, these include but are not limited to simulations of a water crown, a dripping faucet, and a droplet toy.

A fully explicit incompressible smoothed particle hydrodynamics approach for modeling transient heat transfer and thermo-capillary flows

This work presents a Lagrangian meshless method for modeling transient heat transfer and thermo-capillary effects at the interface of two-phase incompressible fluids. To simulate the thermo-capillary effect, we add the Marangoni force to the continuum surface force (CSF) model, by considering the forces caused by the surface tension gradient which acts tangentially to the interface position. In the current study, we extend our previously proposed model which uses a fully explicit incompressible smoothed particle hydrodynamics (EISPH) approach along with corrected SPH and VKF kernel function, to obtain stable and accurate results in non-isothermal single and multi-phase problems.The model is validated for several test cases, including transient heat conduction, natural convection heat transfer, and thermo-capillary droplet migration, against conventional numerical methods. The validated model is used to study the effects of several dimensionless parameters on thermo-capillary droplet migration. The results show that the proposed EISPH method can model accurately complex heat transfer problems such as thermo-capillary induced motion.

A numerical study on wave overwash on viscoelastic floating covers using smoothed particle hydrodynamics

Large floating covers on the water surface, such as very large floating platforms or ice covers in the marginal ice zone, can exhibit viscoelastic response during their interactions with progressive gravity waves. When the wave magnitude is exceedingly large, overtopping can also occur with wave overwash appearing on top of the cover. In the present study, we investigate the numerical simulations of the transient wave overwash on the viscoelastic floating cover using the smoothed particle hydrodynamics (SPH) approach. In particular, a new numerical scheme is derived whereby the floating cover is represented through discretization into elementary rigid sections interconnected via rotational hinges with damping, with the hinge characteristics matching the viscoelastic properties of the cover. Both laminar viscosity and sub-particle-scale turbulence model for the water motion are considered in the SPH simulation. For validation, experiments of wave interaction with a viscoelastic floating cover with and without wave overtopping were also performed in the present study. The results show that SPH can predict well the wave reflection and transmission by the floating cover with transient overwash on top, as well as the threshold of incident wave steepness that initiates the wave overtopping. Overall, the current study demonstrates for the first time that SPH approach can be an effective tool to solve hydro-viscoelasticity problems by simulating the highly complex wave interactions with viscoelastic floating covers including overtopping.

Prediction modeling of coastal sediment transport using accelerated smooth particle hydrodynamics approach

A GPU-accelerated 3D smooth particle hydrodynamics (SPH) scheme is developed and applied to a coastal multi-phase liquid-sediment interaction and sediment transport. The SPH scheme's meshless design and the sediment's particle structure enable the modeling of the waves' interactions with the sediment particles beyond the limitation of the mesh-based methods. A Newtonian constitutive model is used to model the liquid phase, and the sediment transport is formulated based on the Herschel-Bulkley-Papanastasiou (HBP) model. The yield characteristics of the sediment phase are estimated using the Drucker-Prager yield criterion. Due to the parallelization of the solution on graphics processing units, the 3D SPH scheme's performance, which uses millions of particles, is improved. Good correlations were observed in the SPH predictions and experimental measurements, with a maximum difference of 4.85 %. The validated scheme is applied to formulate forecasting models for the coastline sediment transport. It is found that erosion and scouring are expected at the coastline region inclined to the direction of the sea waves, with a predicted mass erosion of about 60e3 kg in four years. The wave's velocity is also established to be directly proportional to the sediment transport. The proposed multi-phase SPH methodology is proven effective for sediment transport prediction.

A multi-scale model for use in hydrodynamic simulations of impacts and hypervelocity penetrations into porous silica aerogel

Low-density silica aerogel is an ideal material for capturing hypervelocity interplanetary dust. To investigate the behavior of hypervelocity shock waves at different particle velocities using silica aerogel densities ranging from 80 kg/m3 to 320 kg/m3, a multi-scale Smooth Particle Hydrodynamics (SPH) approach is employed. The simulation results demonstrate a good agreement with the macroscopic experimental findings across a wide range of particle velocities, from 0.5 km/s to 20 km/s, while considering the shock wave velocities of the porous material and their linear variation. In addition, simulations of pressure-specific volume curves were conducted using the microscopic model. According to the simulation results, we present a novel compression model of silica aerogel materials regarding the classical form of the P−V relationship for porous materials. Building upon the microscopic model, we propose a macroscopic equivalent model for dynamic compression of low-density aerogel, which is subsequently incorporated into the hydrodynamic calculation of interplanetary dust hypervelocity penetration into aerogel. The results of the simulation of hypervelocity penetration indicate that the multi-scale model presented in this work can be used to simulate the macroscopic mechanical behavior of aerogels in a non-uniform field.

Smoothed Particle Hydrodynamics Approach for Simulation of Non-Newtonian Flow of Feedstocks Used in Powder Injection Molding

The present work aims to explore the ability to simulate flow patterns and the velocity field in the powder injection molding (PIM) process using the smoothed particle hydrodynamics (SPH) method. Numerical simulations were performed using the DualSPHysics platform. A feedstock formulated from 17-4 PH stainless steel powder (60 vol. % of powder) and a wax-based binder system was prepared to experimentally obtain its rheological properties that were implemented in DualSPHysics using two different viscosity models. The numerical simulations were calibrated, and then validated with real-scale injections using a laboratory injection press. During the calibration step, the feedstock flow momentum equation in the DualSPHysics code was modified and boundary friction coefficients at different injection rates were adjusted to create a frictional effect. During the validation step, these calibrated conditions were used to simulate the flow behavior into a more complex shape, which was compared with experimental measurements. Using an appropriate boundary friction factor, both the frictional effect of the boundaries and the stability of the numerical solution were taken into account to successfully demonstrate the ability of this meshless SPH method. The flow front length and feedstock velocity obtained in a complex cavity were satisfactorily predicted with relative differences of less than 15%.

An adaptive multi-resolution SPH approach for three-dimensional free-surface flow with fluid impacting

This paper presents a new adaptive multi-resolution smoothed particle hydrodynamics (SPH) approach for simulating three-dimensional free surface flows with fluid impacting. The governing equations for multi-resolution SPH are derived based on the finite particle method (FPM) particle interpolation, which is an alternative SPH formulation for improving interpolation accuracy in the non-uniform particle distribution. A variable kernel length related to the volume of neighbor particles is proposed to control the numerical instability due to the multi-resolution scheme. In adaptive particle refinement (APR), a concept named as continuously-variable characteristic length (CCL) for each particle is defined to determine the splitting or merging scheme and then build a smoothing non-uniform particle distribution. Three-dimensional examples are conducted to validate the presented new APR approach, and the capability and numerical efficiency of the proposed numerical model are verified through solving free-surface flow problems with middle and low Weber numbers. After validation, a refined simulation of droplet impacting is conducted using the proposed adaptive multi-resolution SPH approach. The results show that the proposed SPH could well adapt to the large deformation of three-dimensional free-surface flow, and only provide a refinement near the free-surface domain.

Smooth particle hydrodynamics: a meshless approach for structural mechanics

This article provides an overview of the smooth particle hydrodynamics (SPH) approach and its mathematical modeling. SPH is a numerical technique based on a mesh-free Lagrangian scheme for evaluating the continuum mechanics problems. This method is suitable in the case of continuum objects undergoing large deformation, as conventional finite element methods are unreliable due to mesh failure and convergence issues. It is a widely used approach in the field of astrophysics, fluid mechanics, structural mechanics, soil mechanics, automobiles, and so on. A numerical example is also considered in this research paper to demonstrate the applicability of the method. The simulation process was achieved using LS-Dyna explicit solver software, and plots related to cutting and thrust forces, von Mises stress, plastic strain, temperature distribution, and so on, were obtained. Also, the effect of Time-Scaling Factor (TSSFAC) on SPH simulations was observed in this research.

SPH approach for stability analysis of soil slope with variable permeabilities

A simulation framework based on meshless method has become an alternative numerical tool to model many deformation problems in geotechnical engineering. Large deformations in the failure zone can alter porosity, permeability etc., which in turn can affect the process of the failure. In this paper, a two-phase model in the framework of Smooth Particle Hydrodynamics (SPH) is introduced to model the interaction between water and soil through drag forces according to Darcy’s law. Changes in soil porosity and associated permeability are automatically adjusted within this framework. Firstly, two different problems i.e., flow through porous media and fluidized bed problem, are investigated to examine the suitability, and stability of the proposed SPH method. Then, the stability analysis of a soil slope under different water level conditions is performed with the strength reduction technique, and the groundwater effect of the slope is simulated. It is found that owing to the negative impact of seepage on soil slope, the horizontal displacement of the slope can be significantly larger. Afterwards, the influence of the variable permeabilities on the slope failure is investigated. The simulation results show that the change in permeability has a slight effect on the slope. Although the calculated safety factor does not change, the sliding distance differs by about 10%. The initial porosity has a large negative influence on the stability of the slope. The developed SPH model has been shown to be a valuable and effective tool for modelling complex problems that are challenging to be addressed with traditional approaches.

Lagrangian particle-based simulation of waves: a comparison of SPH and PFEM approaches

Lagrangian numerical methods are particularly suitable to reproduce flows involving large and rapid deformation of the domain, fluid splitting and coalescence, jets and sprays. The absence of the convective terms in the governing equations avoids numerical diffusion. This paper provides a comparative study between two Lagrangian particle models based on the Smoothed Particle Hydrodynamics (SPH) and the Particle Finite Element Method (PFEM). The description of the methods is provided; features and drawbacks of each method are compared and discussed. The introduced models, which represent widely used advanced analysis tools, are compared and validated in the simulation of five test cases: Two solitary waves, two regular wave trains and a non-linear wave-structure impact. Results from each model are similar and quite close to reference data. Therefore, both models have been validated against new test cases never simulated before, showing that these models can be effectively used for the analysis of regular and non-linear wave with structure impact.

Modeling of co-axial bubbles coalescence under moderate Reynolds regimes: A Bi-phase SPH approach

Phenomena involving bubble flow play a significant role in numerous industrial, natural, and scientific systems. Thus, liquid–gas interfaces must be considered the influence of surface tension and buoyancy. This work analyzes a complete numerical study for bi-fluid flow problems in the deformation evolution of two bubbles coalescing in a viscous liquid. This study discusses diverse configurations of the coalescence bubbles process and their effect on the displacement of the center of mass, velocity, streamlines, and evolution of the morphologies’ deformation. The resulting simulations revealed the process of the coalescence bubbles regarding three stages: approaching, drainage, and rupture of the interface. These steps reach different morphologies, defined as oblate ellipsoid, prolate ellipsoid, and ellipsoidal cap shapes between the trailing, leading, and merging bubbles. Likewise, an approximated bi-phase 2D methodology using the Navier–Stokes equations with Smoothed Particle Hydrodynamics (SPH) method and associated with the Continuous Surface Force (CSF) method was employed to approach the interaction between the bubbles, the surrounding liquid, and cavity walls. This approach with SPH and CSF for fused bubbles and their liquid interaction are validated employing numerical benchmarks in situations with high and moderate regimes of the Reynolds (Re) and Eötvös (Eo) numbers, and different sizes of diameter between coalescence bubbles. Correspondingly, examples of bubbles merging around a liquid owing to gravitational are rarely treated in the literature of mesh-free methods, especially to characterize different viscosity, density and surface tension regimes at the bubble–liquid interface, the effect of the method precision (distance between particles, Δx), the size of the surrounding liquid cavity and the initial distance between lighter domains. According to the bubbles deformation, during the coalescence is observed significant influence of Δx resolution and the cavity size, there are instances of instabilities, such as lateral tails, droplets inside the lighter domain, break-up, and satellite bubble formation. Finally, it is provided a robust numerical study of the coalescence process with a bi-phase SPH for different surfaces tension regimes (5≤Eo≤200), viscosity and density ratios (5≤λ,Φ≤100) and initial conditions in merging bubbles problems with moderates Reynolds numbers (5≤Re≤50).

A density-based WCSPH numerical scheme for investigation of multiphase flows with intricate interfaces at high density ratios

Numerical investigation of multiphase problems having complex interface at high density ratios is one of the numerical challenges associated with particle scattering and divergence. Fewer problems have been performed using density-based smooth particle hydrodynamics (WCSPH) in order to solve complex joint surface currents, and most of the simulations in this field have been performed using incompressible smooth particle hydrodynamics (ISPH). Solving high density flows by smooth particle hydrodynamics is associated with particle dispersion and divergence. Various methods have been used to eliminate the scattering of particles, such as a repulsive force at the interface or the corrected density re-value, but there is a problem of particle disintegration at interface at higher times. Numerical simulations of SPH multiphase problems with high density ratio present divergence and dispersion of soluble particles over time simulation. However, this problem is solved in the current model so that continuity is preserved and provides a more accurate solution over time simulation. In the present work, in order to simulate multiphase flows with complex surfaces and high density ratios fluids investigation, a new density-based smooth particle hydrodynamic approach has been utilized. To prevent the particles scattering at the interface, an incompatible particle removal method is used. In the present study, a particle displacement optimization scheme for regularization at phase interface is created by implementing a two-stage change algorithm to maintain the regular particle distribution continuously and conservatively. In order to investigate the accuracy of the current numerical scheme, it is firstly compared with two-phase Poiseuille flow with three fluids having diverse values of viscosity, Reynolds-Taylor instability, Single Bubble rising in a fully filled container, merging of two bubbles, and Bubble rising in a partially filled container; then it is compared with analytical and numerical solutions.

Modelling of the Process of Extrusion of Dry Ice through a Single-Hole Die Using the Smoothed Particle Hydrodynamics (SPH) Method.

This article presents the outcome of research on modelling the process of the extrusion of crystalline dry ice. The purpose of this process is to densify the material and obtain pellets of several millimeters in diameter. This reduces the sublimation rate in ambient conditions of the material whose temperature in a solid state is 195 K. A lower sublimation rate means a reduction of the loss of product in its final applications, which include refrigeration and reduction of atmospheric emissions of gaseous CO2. A ram-type extruder was considered in this analysis, in which dry ice was extruded through a single-hole die of varying geometry. The article presents the results of numerical analyses of the extrusion process, using a simulation method based on the Smoothed Particle Hydrodynamics (SPH) approach. The results from simulations were verified by the experimental data in terms of the maximum force required to complete the process, in order to assess the applicability of the proposed method in further research on dry ice compression.

Numerical investigation of the influence of casting techniques on fiber orientation distribution in ECC

Engineered cementitious composites (ECC), also known as bendable concrete, were developed based on engineering the interactions between fibers and cementitious matrix. The orientation of fibers, in this regard, is one of the major factors influencing the ductile behavior of this material. In this study, fiber orientation distributions in ECC beams influenced by different casting techniques are evaluated via numerical modeling of the casting process. Two casting directions and two casting positions of the funnel outlet with beam specimens are modeled using a particle-based smoothed particle hydrodynamics (SPH) method. In this SPH approach, fresh mortar and fiber are discretized by separated mortar and fiber particles, which smoothly interact in the computational domain of SPH. The movement of fiber particles is monitored during the casting simulation. Then, the fiber orientations at different sections of specimens are determined after the fresh ECC stops flowing in the formwork. The simulation results show a significant impact of the casting direction on fiber orientation distributions along the longitudinal wall of beams, which eventually influence the flexural strength of beams. In addition, casting positions show negligible influences on the orientation distribution of fibers in the short ECC beam, except under the pouring position.

Simulation of sloshing in the moon pool with Smoothed Particle Hydrodynamics

In maritime heavy industry, the moon pool is an opening through the hull of some vessels. We replicate a generic design of the pool with the Lagrangian approach Smoothed Particle Hydrodynamics (SPH) whose mathematical model efficiently simulates the interphasial surface. In this study we present the capability of our in-house SPH code to handle the sloshing in the moon pool. We validate the SPH approach to flows for the sloshing tank benchmark and show the stability of this approach for the non-trivial case of the moon pool.

SPH modeling and investigation of cold spray additive manufacturing with multi-layer multi-track powders

Cold spray (CS), as a new solid-state additive manufacturing technique, involves complex phenomena like high-speed impacting of micro-powders, large material deformations, phase change and jet generation. The CS process is difficult to be accurately simulated, and the underlying coating mechanisms, especially for multi-powders CS, have not been well understood. As a Lagrangian and particle method, the smoothed particle hydrodynamics (SPH) method has natural advantages in treating large deformations and capturing moving interfaces. In this work, we present an improved SPH approach to implement three-dimensional particle modeling and study of the multi-layer multi-track CS problem. The kernel gradient correction (KGC), adaptive smoothing length and the constitutive model are integrated in the improved SPH. The contour profile and width thickness ratio of the deformed powder obtained by the present simulation are very close to the experimental results. The bonding behaviors in a single powder CS with different materials are first explained where the critical velocities for different materials are obtained. Furthermore, coating behaviors in CS with different layers and tracks of powders are comprehensively analyzed. Some typical deformation parameters of the powders track with regard to an increasing impacting velocity are attained. With the present numerical model, a larger scale multi-layer multi-track CS is promising to be reproduced with some parameter windows predicted, which is greatly helpful to CS operations.

A fully explicit incompressible Smoothed Particle Hydrodynamics method for multiphase flow problems

Multiphase flow is a challenging area of computational fluid dynamics (CFD) due to their potential large topological change and close coupling between the interface and fluid flow solvers. As such, Lagrangian meshless methods are very well suited for solving such problems. In this paper, we present a new fully explicit incompressible Smoothed Particle Hydrodynamics approach (EISPH) for solving multiphase flow problems. Assuming that the change in pressure between consecutive time-steps is small, due to small time steps in explicit solvers, an approximation of the pressure for following time-steps is derived. To verify the proposed method, several test cases including both single-phase and multi-phase flows are solved and compared with either analytical solutions or available literature. Additionally, we introduce a novel kernel function, which improves accuracy and stability of the solutions, and the comparison with a well-established quintic spline kernel function is discussed. For the presented benchmark problems, results show very good agreements in velocity and pressure fields and the interface-capturing with those in the literature. To the best knowledge of the authors, the EISPH method is presented for the first time for multiphase flow simulations.

A smoothed particle hydrodynamics approach for phase field modeling of brittle fracture

Fracture is a very challenging and complicated problem with various applications in engineering and physics. Although it has been extensively studied within the context of mesh-based numerical techniques, such as the finite element method (FEM), the research activity within the Smoothed Particle Hydrodynamics (SPH) community remains scarce. SPH is a particle-based numerical method used to discretize equations of continuum media. Its meshfree nature makes it ideal to simulate fracture scenarios that involve extreme deformations. However, to model fracture, SPH researchers have mostly relied on ad-hoc empirical local damage models, cohesive zone approaches, or pseudo-spring models, which come with a set of drawbacks and limitations. On the other hand, phase field models of brittle fracture have recently gained popularity in academic circles and provide significant improvements compared to previous approaches. These improvements include the derivation from fundamental fracture theories, the introduction of non-locality, and the ability to model multiple crack initiation, propagation, branching, and coalescence, in situations where no prior knowledge of the crack paths is available. Nevertheless, phase field for fracture has not been studied within SPH. In this proof-of-concept paper we develop and implement a phase field model of brittle fracture within the context of SPH. Comprehensive mathematical and implementation details are provided, and several challenging numerical examples are computed and illustrate the proposed method’s ability to accurately and efficiently simulate complex fracture scenarios.