Proposed Smoothed Particle Hydrodynamics Model 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.

Wave interactions with multi-float structures: SPH model, experimental validation, and parametric study

This paper proposes a new type of multi-float structures which comprise several serially arranged box-type modules. Adjacent modules are connected at the top corners using hinges, while rubber bumpers are placed at the bottom corners to absorb the collision energy. The whole structure is anchored to the seabed with mooring lines. A Smoothed Particle Hydrodynamics (SPH) model is established to study the wave interactions with such multi-float structures. In the SPH model, the Navier-Stokes equations are solved for the wave motion and the multi-degree-of-freedom motion of the structure is tracked by applying the Newton's second law to rigid bodies. A light spring model is used to evaluate the mooring forces, while the collision forces between adjacent modules are calculated according to the force-compression relation of the rubber bumpers. Besides, a continuity restriction on the linear acceleration is applied to the hinge connectors between adjacent modules. To validate the proposed SPH model, a laboratory experiment is conducted regarding the hydrodynamic performance of a three-float structure. Then, the SPH model is applied to a multi-float design scenario, from which useful findings have been obtained for engineering practice.

Simulation of non-cohesive soil turning based on an SPH model

Soil turning is an infrastructure activity in the field of geotechnical engineering. In this study, we propose a new soil turning numerical model based on the Smoothed Particle Hydrodynamics (SPH) method, in which an elastoplastic constitutive model is implemented. To validate the model, firstly, a landslide benchmark test is studied, the error of the maximum sliding distance is only 1.5 % compared to the experimental data. Next, a combined experimental numerical investigation on the soil turning process is carried out. We compare the experimental observations with the numerical modeling results and find that the numerical error of the peak height and the horizontal distance of the soil is about 2.56 % and 3.37 %, respectively, indicating that the proposed SPH model can reproduce the soil turning process accurately. The simulation results also demonstrate that: (1) When the turning speed is increased, the turning resistance does not change significantly but leads to a more sufficient mixing of the soil; (2) There exists a critical turning angle above which the resistance increase significantly associates with a larger angle; (3) Increasing the burying depth of the tool helps to improve the mixing effect; however, leads to larger resistance as well.

Smoothed particle hydrodynamics method for pinch plasma simulation with non-ideal MHD model

When plasma is compressed by magnetic forces, a pinch phenomenon is observed. Pinch plasma has received significant attention as an efficient source of radiation and a way for high-density plasma physics analysis. In this study, a non-ideal magnetohydrodynamics (MHD) model is applied to a smoothed particle hydrodynamics (SPH) framework to analyze pinch plasmas whose local resistivity varies with temperature and pressure. The proposed SPH model incorporates several numerical treatments, such as a correction term to satisfy the ∇·B constraint and some artificial dissipation terms to govern the shock wave. Moreover, it includes the evaluation of a novel SPH discretization for non-ideal MHD terms, including current density calculations. Furthermore, the proposed model is validated with three benchmark cases: (1) Brio and Wu shock tube (ideal MHD), (2) resistive MHD shock simulation, and (3) magnetized Noh Z-pinch problem. The simulation results are compared with the results of some reference Eulerian MHD simulations and analytical solutions. The simulations agree well with the reference data, and the introduced numerical treatments are effective. Finally, X-pinch simulations are performed using the proposed model. The simulations well produce the micro Z-pinch and jet shapes, which are important X-pinch features. Overall, the proposed SPH model has extensive potential for studying the complex pinch plasma phenomena.

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.

A general SPH framework for transient seepage flows through unsaturated porous media considering anisotropic diffusion

The Smoothed Particle Hydrodynamics (SPH) method has become a popular numerical tool to solve many challenging engineering applications. However, its application to solving anisotropic transient unsaturated–saturated seepage flow problems is still absent in the literature. Among several challenges involved in solving this important problem, the lack of a robust and general SPH formulation to obtain accurate approximations of second derivatives on disordered particle system is the key obstacle preventing this to happen. In this paper, we first propose a general SPH formulation for the second derivatives, capable of considering anisotropic diffusions, and demonstrate that the new formulation outperforms existing SPH formulations for the second derivatives and achieves high accuracy on the highly disordered particle systems. Subsequently, we utilise this newly developed SPH formulation to tackle the transient seepage flows through porous media for the first time, considering anisotropic flows and complete time-dependent transition from unsaturated to saturated states and vice-versa. This naturally leads to a general SPH framework for solving transient seepage problems in unsaturated/saturated porous media using one set of Lagrangian particles (or Lagrangian discretisation). Robust boundary conditions and their implementations for solving general seepage problems in SPH are also proposed, enabling the proposed SPH model to automatically capture seepage surface (including the free surface of unconfined seepage) without any difficulty or ad hoc treatment. Moreover, a simple method to generate a random particle system suitable for SPH simulations on large scale problems using the Voronoi tessellation technique is proposed to study transient seepage problems for the first time. Several verification examples are presented to demonstrate the capabilities of the proposed SPH framework in solving the complex seepage flow problems, including those on multi-resolution particle configurations. Excellent agreements with a wide range of numerical and theoretical solutions are achieved, suggesting that the newly proposed SPH model can be applied to solve complex transient seepage flow problems. This marks an important milestone for the future development of SPH to solve fully coupled flow deformation problems involved large deformation and failure of porous media, which are challenging for the most state-of-the-art mesh-based numerical methods.

Numerical Investigation of Surge Waves Generated by Submarine Debris Flows

Submarine debris flows and their generated waves are common disasters in Nature that may destroy offshore infrastructure and cause fatalities. As the propagation of submarine debris flows is complex, involving granular material sliding and wave generation, it is difficult to simulate the process using conventional numerical models. In this study, a numerical model based on the smoothed particle hydrodynamics (SPH) algorithm is proposed to simulate the propagation of submarine debris flow and predict its generated waves. This model contains the Bingham fluid model for granular material, the Newtonian fluid model for the ambient water, and a multiphase granular flow algorithm. Moreover, a boundary treatment technique is applied to consider the repulsive force from the solid boundary. Underwater rigid block slide and underwater sand flow were simulated as numerical examples to verify the proposed SPH model. The computed wave profiles were compared with the observed results recorded in references. The good agreement between the numerical results and experimental data indicates the stability and accuracy of the proposed SPH model.

Large deformation analysis of granular materials with stabilized and noise-free stress treatment in smoothed particle hydrodynamics (SPH)

This paper presents a new smoothed particle hydrodynamics (SPH) model for the large deformation analysis of granular materials with improved accuracy and stability. In order to remove the spurious stress profile during the post-failure process which is a common issue for the application of SPH to geotechnical problems, an innovative stress diffusion term is formulated. Further a new boundary treatment is proposed with the use of renormalization techniques to give a first-order consistent wall boundary conditions for geotechnical applications. This methodology is able to deal with complex geometries such as sharp corners. A number of test cases are considered to examine the robustness and accuracy of the proposed technique. Results show that the new boundary formulation is able to improve the accuracy of the solution even for a relatively coarse particle resolution. The stress diffusion term reduces the numerical noise that affects the stress under large deformations, resulting in a smooth stress field. The proposed SPH model is finally applied to the simulation of granular flow and tunnel face collapse, showing satisfactory agreement and convergence with experimental results.

Theoretical modeling and experimental analysis of single-grain scratching mechanism of fused quartz glass

Abstract Surface and subsurface damage, including cracks, scratches, microcracks, and residual stress, is inevitable when fabricating fused quartz glass because of their high brittleness and low fracture toughness. Single-grain scratching mechanism of fused quartz glass is examined using smoothed particle hydrodynamics (SPH) to clarify the mechanisms of material removal and produce crack-free optical surfaces. Single diamond grain experiments were conducted to validate the proposed SPH model, which predicts the critical depth of approximately 0.20 μm for ductile–brittle transition in fused quartz glass. Both simulation and experimental results indicate that three removal regimes, namely, complete ductile, ductile–brittle transform, and complete brittle modes, are involved in the material removal process. SPH simulation helps identify the location of crack formation and morphology of crack propagation during scratching. Thus, the SPH model is used to simulate the single grain scratching process under different conditions. Simulation results reflect that changing the scratching speed will lead to a remarkably different mechanism of crack initiation and propagation compared with changing the scratching depth. Effects of scratching depth and speed on scratching force and residual stress are also discussed thoroughly in the simulation analysis.

SPH model for interaction of sloshing wave with obstacle in shallow water tank

The violent fluid motion in a partially filled vessel is called sloshing. Resonance occurs when the natural frequency of the fluid oscillation approaches that of its container. This result may lead to structural failure. In this study, a Smoothed Particle Hydrodynamics (SPH) model is established to investigate the sloshing motion in a shallow water reservoir. Sloshing in a submerged obstacle, cylinder array, rectangular and wall-inclined topography is considered. In terms of results, the cylinder array is more effective than the other models to reduce the impact force due to the sloshing wave in a rectangular tank. The results prove that the proposed SPH model is capable of simulating sloshing in the shallow water tank.

Smoothed Particle Hydrodynamics multiphase modelling of an experimental microfluidic device for conformal coating of pancreatic islets

The paper discusses a Smoothed Particle Hydrodynamics (SPH) model for the analysis of the multiphase flow occurring in an experimental microfluidic device for conformal coating of pancreatic islets with a biocompatible and permeable polymer. The proposed numerical model, based on a weakly-compressible SPH approach, accurately mimics the encapsulation process while assuring phase conservation, thus overcoming potential limitations of grid-based models. The proposed SPH model is a triphasic multi-phase model that allows one: (i) to reproduce the physics of islet conformal coating, including the effects of surface tension at the interface of the involved fluids and of the islet diameter; and (ii) to evaluate how modulation of process parameters influences the fluid dynamics within the microfluidic device and the resulting coating characteristics. This model can represent a valuable, time- and cost-effective tool for the definition of optimized encapsulation conditions through in silico screening of novel combinations of conformal coating parameters, including polymeric coating blends, size range of insulin-secreting cell clusters, utilized chemical reagents, device geometry and scale.

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.

SPH-based analysis of the post-failure flow behavior for soft and hard interbedded earth slope

This study proposed a Smoothed Particle Hydrodynamics (SPH) model that could consider two types of soils with different viscosities to reveal the flow mechanism of a soft and hard interbedded earth slope. The flow processes of an actual unstable slope in the Lushan hot spring district and the Saleshan landslide were simulated, and the applicability of proposed SPH model was validated by comparing the flow process and the flow velocity with DEM results and surveyed data. Thereafter, with a conceptual simulating case for the soft and hard interbedded earth slope, materials were divided into two types, and eight groups consisting of 64 cases were analyzed with different viscosities. According to the variation curves of the run-out and the flow velocity with time, the flow behavior is controlled by the properties of both the soft layer and hard layer, and increasing the viscosity of the hard layer can greatly reduce the run-out and the maximum velocity. The result provided a basis for the mitigation of possible layered earth slope disasters in engineering geology.

Effect of Porous Media on Hydraulic Jump Characteristics by Using Smooth Particle Hydrodynamics Method

In order to understand the effect of porous media on hydraulic jumps, a smoothed particle hydrodynamics (SPH) model is applied to investigate the characteristics of hydraulic jumps interacting with porous media. Various porosities including cases without an obstacle or with a solid obstacle or porous media are considered. The opening of a gate was altered to adjust the hydraulic jump. The conjugate depth ratio, bottom shear stress distribution, and energy dissipation are reported. In the present study, validations are in a good agreement with previous studies. Overall, the result showed that the average error between numerical and experimental data was less than 7.2%. Energy dissipation is compared among cases with three porosities, with and without a solid obstacle. The porosity of 0.68 is found to dissipate more energy than do other porosities. Thus, porous media can be used to enhance energy dissipation of hydraulic jumps in an open channel. In conclusion, the proposed SPH model can simulate the effect of porous media on hydraulic jump characteristics.

A numerical study on ice failure process and ice-ship interactions by Smoothed Particle Hydrodynamics

In this paper, a Smoothed Particle Hydrodynamics (SPH) method is extended to simulate the ice failure process and ice-ship interactions. The softening elastoplastic model integrating Drucker-Prager yield criterion is embedded into the SPH method to simulate the failure progress of ice. To verify the accuracy of the proposed SPH method, two benchmarks are presented, which include the elastic vibration of a cantilever beam and three-point bending failure of the ice beam. The good agreement between the obtained numerical results and experimental data indicates that the presented SPH method can give the reliable and accurate results for simulating the ice failure progress. On this basis, the extended SPH method is employed to simulate level ice interacting with sloping structure and three-dimensional ice-ship interaction in level ice, and the numerical data is validated through comparing with experimental results of a 1:20 scaled Araon icebreaker model. It is shown the proposed SPH model can satisfactorily predict the ice breaking process and ice breaking resistance on ships in ice-ship interaction.

Cylindrical Smoothed Particle Hydrodynamics Simulations of Water Entry

This paper presents a smoothed particle hydrodynamics (SPH) modeling technique based on the cylindrical coordinates for axisymmetrical hydrodynamic applications, thus to avoid a full three-dimensional (3D) numerical scheme as required in the Cartesian coordinates. In this model, the governing equations are solved in an axisymmetric form and the SPH approximations are modified into a two-dimensional cylindrical space. The proposed SPH model is first validated by a dam-break flow induced by the collapse of a cylindrical column of water with different water height to semi-base ratios. Then, the model is used to two benchmark water entry problems, i.e., cylindrical disk and circular sphere entry. In both cases, the model results are favorably compared with the experimental data. The convergence of model is demonstrated by comparing with the different particle resolutions. Besides, the accuracy and efficiency of the present cylindrical SPH are also compared with a fully 3D SPH computation. Extensive discussions are made on the water surface, velocity, and pressure fields to demonstrate the robust modeling results of the cylindrical SPH.

Simulation of Sea-ice Thermodynamics by a Smoothed Particle Hydrodynamics Method

Abstract The paper deals with the problem of sea-ice pack motion and deformation under the action of wind and water drag forces. Differential equations describing the behaviour of ice, with its very distinct material responses in converging and diverging flows, express the mass and linear momentum balances on a horizontal plane (the free surface of the ocean). The thermodynamic effects (ice melting and lead water freezing) are accounted for by adding source terms to the equations describing the evolution of the ice thickness and area fraction (concentration). These thermodynamic source terms are described by means of a single function that idealizes typical ice growth-rates observed in winter in the Arctic. The equations governing the problem are solved by a fully Lagrangian method of the smoothed particle hydrodynamics (SPH). Assuming that the ice behaviour can be approximated by a non-linearly viscous rheology, the proposed SPH model was used to simulate the flow of a sea-ice pack driven by wind drag stresses and varying seasonal temperatures. The results of numerical simulations illustrate the evolution of an ice pack, including distributions of ice thickness and ice area fraction in space and time for assumed temperature distributions.

An Algorithm for Fluid–Solid Coupling Based on SPH Method and Its Preliminary Verification

Based on the fundamental theory of smoothed-particle hydrodynamics (SPH), a feasible algorithm for fluid–solid coupling on interface is applied to describe the dynamic behavior of fluid and solid by utilizing continuum mechanics governing equations. Numerical simulation is conducted based on the proposed SPH model and the fluid–solid interface coupling algorithm, and good agreement is observed with the experiment results. It is shown in the results that the present SPH model is able to effectively and accurately simulate the free-surface flow of fluid, deformation of the elastic solid and the fluid–solid impacting.

Generalized Fickian approach for phase separating fluid mixtures in Smoothed Particle Hydrodynamics

In the preparation process of porous polymer membranes, multi-component mass transfer during phase separation leads to the formation of pores. In this paper, we study the Generalized Fickian approach for a phase separating ternary fluid mixture using the Smoothed Particle Hydrodynamics (SPH) method. The thermodynamics are based on the Flory–Huggins equation of state for polymer mixtures with different molar weight and density of the components.We present a validation of the discrete balance equation and study the effect of different molar weight and density on the accuracy of the method separately by considering phase separation in a periodic box in two dimensions. We analyze the mass fraction distribution and the time-evolving reduction of the amount of interface using a mapping scheme based on the rheological Doi–Ohta model. We find good agreement with the diffusion-dominant power law for coarsening. Finally, we apply the proposed SPH model on a realistic Polyvinylidenfluorid/Dimethylformamid/water system. The corresponding, composition-dependent diffusion coefficients are estimated using molecular dynamics simulations.

A Development of a SPH Model for Simulating Surface Erosion by Impact(s) of Irregularly Shaped Particles

Modeling and studying the impact of angular particles are very helpful in understanding the fundamental mechanisms of erosive wear. However, the majority of previous studies focused on well-defined symmetrical particles, which are not well representative of the abrasive particles. Hence, this study develops a mesh-free model based on the smoothed particle hydrodynamics (SPH) method to simulate impact(s) of single and multiple irregularly shaped particles on ductile material. A novel procedure is proposed to model the particle as a polygonal rigid body through measuring the corner vertices. Simulations are carried out by varying the input conditions and by using different types of angular particles. Common erosion mechanisms such as cutting, machining, ploughing, prying-off are successfully reproduced by the model. The predicted crater is compared with available experimental data, and good agreement has been achieved. The proposed SPH model and out present study could be useful in the study of erosive wear on the surface of metal devices that carries granular substances.