Two-dimensional Smoothed Particle Hydrodynamics Research Articles

Chaotic advection of fluid particles at different Reynolds numbers by two-dimensional smoothed particle hydrodynamics

Chaotic advection of fluid particles at different Reynolds numbers by two-dimensional smoothed particle hydrodynamics

Complex dam break simulation using the 2-D depth-averaged SPH flow model: a validation for tsunami application

Dam break flow has a similar characteristic to the tsunami surge after the breaking wave. Therefore, it is often used in laboratory-scale experiments to study tsunamis and can be used as a benchmark for validating a numerical model. This paper presents a simulation of a complex dam break flow to validate the two-dimensional (2-D) depth-averaged Smoothed Particle Hydrodynamics (SPH) flow model which involves a non-submersible obstacle in the domain. The method can also be referred to as shallow-water equations SPH (SWE-SPH). With SPH, the wetting and drying interfaces are automatically solved without any additional trick or handling. Therefore, a dry bed dam break is specifically tested here. The numerical results are validated using experimental data from the literature. The model shows the ability to reproduce the flow fields, shocks, vortices and flow region transitions with reasonable accuracy compared to the experimental data, despite the vertical averaging process in the formulation. This model can be a robust tool for predicting the hazards caused by extreme floodings, such as dam breaks, flash floods and tsunamis in development planning.

Two-dimensional smoothed particle hydrodynamics (SPH) simulation of multiphase melting flows and associated interface behavior

ABSTRACT Heat transfer and phase change in multiphase media involve complex behavior such as multi-physics coupling, unsteady interfaces, and boundary generation/disappearance. The smoothed particle hydrodynamics (SPH) method is used to simulate multicomponent problems (initially solid material surrounded by a fluid) characterized by heat transfer, solid–liquid phase change, and multiphase flow. First, the interface behavior of the melted liquids and ambient fluids are simulated by a multiphase SPH model, where corrected algorithms and techniques are adopted to provide a stable simulation for the interface with a large density ratio. The wetting effect of the solid surface by melted liquids is considered by extending the continuum surface force model to three phases including solid, melted liquid and ambient fluid. Second, a thermal dynamics model is incorporated with the multiphase SPH model. The solid–liquid phase change occurs in a small temperature interval in which the latent heat is incorporated using the equivalent heat capacity. Third, the numerical model is validated using several benchmark examples. Five specially configured cases are simulated to demonstrate the robustness, adaptability, and stability of the model. The intriguing phenomena of evolution of the fluid interface of melted liquids, accumulation of thin-layer liquids, and melted droplet formation are reproduced.

Euler–Lagrange framework for deformation of granular media coupled with the ambient fluid flow

A full-scale continuum framework for modeling fluid interaction with granular media is computationally exhaustive due to the diverse range of length and time scales. Given the nature of these processes, the computational burden aggravates the problem of real-time simulation for large-scale scenarios. In the current study, the interaction between Newtonian fluid and deformable granular media is modeled through a coupled framework comprising of a two-dimensional divergence-free Incompressible Smoothed Particle Hydrodynamics and a depth-integrated Finite Volume Method, respectively. The coupling is based on the interaction force pair tailored for each module appropriately. The formulation has been validated against a variety of test-cases comprising of a diverse configuration of initial conditions for both fluid and granular modules. The proposed framework is in consonance with experimental data and may be extended to real-time scenarios owing to lower computational overhead.

Two-Dimensional SPH Analysis of Seepage with Water Injection Process for Different Crack Morphologies

Crack seepage in nature involves natural and water injection flow, causing crack morphology in nature to be varied. Using the numerical simulation method of smoothed particle hydrodynamics (SPH), the natural free flow process in a crack was analyzed. With the interference of the initial velocity of the x = 0 particles, the other terminal particles were shifted, and the particles with initial velocities were reversed. For water injection simulations, ghost particles were set to block particles from overflowing, as particles subjected to injection water were mobilized more quickly than under free flow conditions. For rough cracks, particle magnitude was affected by the boundary shape, but overall particle velocity was influenced little, and the distribution of particles was sparse and densely spaced. For the branch crack simulation, overall particle seepage velocity decreased, but particles moved faster through the wider branch than through the narrower branch. SPH can simulate the seepage through crack networks and be used to analyze the effects of different crack geometries and physical properties.

A novel interface method for two-dimensional multiphase SPH: Interface detection and surface tension formulation

A novel interface method is developed in this paper for two-dimensional smoothed particle hydrodynamics (SPH) modelings of multiphase flows. The present interface method aims to resolve two essential issues in the multiphase flow simulations: the interface detection and the implementation of surface tension force. Specifically, a novel and easy-to-implement algebraic indicator is proposed to detect the interface particles. And the surface tension force is locally implemented on the interface particles by reconstructing arc lines connecting three adjacent interface particles. Compared with the previous surface reconstruction method, the present method utilizes fewer particles in the local evaluation of surface tension. The novel algebraic indicator provides more accurate and efficient detection of the interface particles, especially for the sparse or aggregated particle distributions. In the meantime, the present surface tension formulation removes the tedious process of evaluating gradient of the color index and thus significantly improves the numerical efficiency. The accuracy, flexibility and efficiency of the present interface method are comprehensively evaluated through four numerical examples, namely the sloshing in a rectangular tank, oscillation of elliptic droplet, Laplace law for a stationary droplet, and air bubble rising in water. The good agreement of the present numerical results with the published results demonstrates that the novel interface method proposed in this paper can precisely detect the interface particles with appealing sharpness, and recover the surface tension force accurately and efficiently.

Numerical Analysis of Unsteady Behavior of Cloud Cavitation and Its Induced Shock Waves by Two-Dimensional Smoothed Particle Hydrodynamics Method

Numerical Analysis of Unsteady Behavior of Cloud Cavitation and Its Induced Shock Waves by Two-Dimensional Smoothed Particle Hydrodynamics Method

Impact simulation and ballistic analysis of B4C composite armour based on target plate tests

Lightweight composite armour systems composed of a B4C ceramic panel and composite back panel have excellent bulletproof performance and are used to resist attacks from armour-piercing incendiary projectiles. Numerical simulations can be used to simulate the process of projectiles impacting armour; thus, this method is widely used in armour ballistic performance analyses. To verify the accuracy of the B4C material model, a finite element method based on two-dimensional smoothed particle hydrodynamics is used to simulate the penetration process of steel projectiles into B4C/Al composite armour. To verify the accuracy of the ultra-high molecular weight polyethylene (UHMW-PE) model, a three-dimensional Lagrange method was used to simulate the penetration of a fragment simulating projectile into the UHMW-PE. The influence of geometric strain in the erosion algorithm on the ballistic performance of the UHMW-PE was investigated, and the erosion geometric strain suitable for the UHMW-PE was identified. The impact of a 12.7 mm armour-piercing incendiary projectile on the B4C/UHMW-PE and B4C/C/UHMW-PE armours was then simulated and tested experimentally. The results showed that the B4C/UHMW-PE armour was penetrated by the projectile, while the B4C/C/UHMW-PE armour was not penetrated. The ballistic performance of the B4C composite armour, damage state of the B4C ceramic, and bulge deformation of the UHMW-PE were accurately obtained in the simulations. A comparison with the experimental results showed that the proposed method could accurately simulate the penetration process of the B4C/UHMW-PE armour, reveal the penetration mechanism of composite armour, reduce the number of projectile tests, and provide a basis and technical means for the design and optimisation of lightweight composite armour.

A multiphase SPH framework for solving the evaporation and combustion process of droplets

PurposeThis paper aims to introduce a two-dimensional smoothed particle hydrodynamics (SPH) framework for simulating the evaporation and combustion process of fuel droplets.Design/methodology/approachTo solve the gas–liquid two-phase flow problem, a multiphase SPH method capable of handling high density-ratio problems is established. Based on the Fourier heat conduction equation and Fick’s law of diffusion, the SPH discrete equations are derived. To effectively characterize the phase transition problem, inspired by volume of fluid method, the concept of liquid phase mass fraction of the SPH particles is proposed. The one-step global reaction model of n-hexane is used for the vapor combustion.FindingsThe evaporation and combustion process of single droplet conforms to the law. The framework works out well when the evaporation of multiple droplets involves coalescence process. Three different kinds of flames are observed in succession in the combustion process of a single droplet at different inflow velocity, which agree well with the results of the experiment.Originality/valueTo the best of the authors’ knowledge, this is the first computational framework that has the capability to simulate evaporation and combustion with SPH method. Based on the particle nature of SPH method, the framework has natural advantages in interface tracking.

Numerical Analysis of Unsteady Phenomena of Cloud Cavitation by the Two-dimensional Smoothed Particle Hydrodynamics Method

Numerical Analysis of Unsteady Phenomena of Cloud Cavitation by the Two-dimensional Smoothed Particle Hydrodynamics Method

Interaction analysis between waves and perforated caisson using the revised smoothed particle hydrodynamics method and finite element method

A two-dimensional smoothed particle hydrodynamics analysis model based on Riemann solution is put forward to discuss its application for the wave-perforated caisson interaction problem. The wave particles are simulated by the smoothed particle hydrodynamics method and the perforated caisson employs the finite element method. The numerical method has been verified by comparing the process of elastic plate with liquid tank with test, and a good agreement is reached. Then, the proposed method is employed to study the distribution of dynamic stress in the perforated plate position of dissipation chamber at the still water level, as well as the distribution of dynamic stress along the perforated plate. Furthermore, the relationship between the dynamic stress and the corresponding coefficient is also discussed, such as the relative width B/L of dissipation chamber of no-roof perforated caisson and the relative height s/L of top cover of perforated caisson. This article concludes by providing reference to the design and construction of perforated caisson breakwaters.

Numerical modeling of flexible floating boom using a coupled SPH–FEM model

ABSTRACTA two-dimensional smoothed particle hydrodynamics–finite-element method (SPH-FEM) model is developed to model the movement of flexible floating boom and bending of its skirt under sea environment. The most significant feature of the present model is the introduction of a weakly coupled gird-to-particle interface for bridging the SPH domain of fluid and the FEM domain for resolving the deformation of the flexible boom skirt, which is different from the previous simulation that adopts a rigid module and flexible connector approach of multibody system. The SPH–FEM model is validated against a series of experimental tests of boom motion and skirt deformation. A comprehensive investigation is concentrated on the hydrodynamic characteristics of the floating booms for using different material stiffness and skirt length under the action of combined wave current. It is found that the boom with longer skirt does not necessarily have good containment performances due to its poor hydrodynamic property in terms of heave and roll. Moreover, the flexible floating boom is proved to have better oil containment performance than the rigid one in a wave-dominated environment. It is also found from the FEM solution of the skirt deformation that the maximum principal strain mainly occurs in the vicinity of the floater–skirt joint on the leeside surface of the skirt under the action of combined waves and currents.

Perforation of Steel Targets by Blunt Projectiles Using Smoothed Particle Hydrodynamics Method

In this paper, perforations of 12[Formula: see text]mm thick Weldox 460E steel plates by 20[Formula: see text]mm diameter blunt projectiles are simulated based on Two-dimensional Smoothed Particle Hydrodynamics method (SPH), and the modified Johnson–Cook (MJC) material model is adopted. To describe the shear plugging process, the particle approximation between different materials is canceled, and only the particle contact model based on the principle of conservation of momentum is applied. Then the separation of projectile and plug is simulated successfully, which is consistent with the experimental observations. Furthermore, it can be found that the particle size has a great influence on the calculation by comparing the effects of the different SPH particle sizes on plugging calculations. In general, the smaller the particle size is, the greater the residual velocity of projectile is. The residual velocities are tending towards stability as the decrease of particle size. Taking computational efficiency and accuracy into consideration, 0.033 (size[Formula: see text][Formula: see text][Formula: see text]0.4[Formula: see text]mm) is the most appropriate dimensionless particle size. Then, the effect of target thickness on perforation is conducted, which shows that the target thickness has certain influence on the global deformation of target. Moreover, the sensitivity of MJC material constants on the residual velocity of projectile is also analyzed and discussed using orthogonal experimental design method and the range analysis method. The results indicate that the most sensitivity parameter is yield strength [Formula: see text], followed by strain hardening modulus [Formula: see text] and strain hardening exponent [Formula: see text].

A fluid simulation method based on two-dimensional smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) method is a kind of meshless method, which is used to solve the problem of fluid simulation without complex operations of the grids. To reduce the computational complexity, SPH method based on the two-dimensional shallow water equations is employed to establish a fluid model. In large scale scenes, taking into account the high computational complexity and the serious distortion problems, in this paper we introduce an improved two-dimensional SPH algorithm according to the shallow water equations. The proposed method with two-dimensional complexity is obtained by discretizing the two-dimensional shallow water equations with SPH, and the depth of water is introduced as the particle's property. The problem of increased amount of calculation cannot be well solved by using traditional neighboring particle search method based on tree structure. To improve the efficiency of search and simplify the search operation of neighborhood particles, in this paper we introduce a point-in-box search algorithm and put forward a neighboring particles searching method on the basis of dynamic grid. Besides, for large scale scenes, by considering that the virtual particle method provides slow computation speed with complex boundary condition, the type-one virtual particles are utilized to ensure that the borders can be calculated precisely by combining the punish force to prevent the phenomenon of particle boundary penetrating. Therefore, a method is further obtained to handle boundary condition efficiently by combining the virtual particles with punish force in this paper. In the process of rendering, the fluid surface is first determined by mapping and interpolating particles into regular grids without the complex reconstruction of surface in three-dimensional. Then, we utilize the bilinear interpolation method to deal with the problem of missing values, and the surface grids are further densified. With OpenSceneGraph three-dimensional render engine, OpenGL Shading Language is adopted to speed up the rendering speed, and in this way, the real-time fluid simulation of large scale scenes can be further achieved. With the basic KD tree searching method employed in the simulations, the comparative experiments are provided to verify effectiveness of the proposed searching method based on dynamic grid. Given the data set obtained from random points, experimental results demonstrate that the method in this paper can be used to solve the problem of neighboring particles searching in large scale scenes. To show the effectiveness of the proposed method on the basis of the virtual particles and the punish force, another experiment based on the collapsing of a water column is further provided. Besides, in this paper we conduct an experiment on a certain actual reservoir terrain to prove that the proposed method can be applied to fluid simulation of large scale scenes.

SPH Modeling of Hydraulics and Erosion of HPTRM Levee

Post-Katrina investigations revealed that most earthen levee damage occurred on the levee crest and landward-side slope as a result of either wave overtopping, storm surge overflow, or a combination of both. In this paper, combined wave overtopping and storm surge overflow of a levee embankment strengthened with high performance turf reinforcement mat (HPTRM) system was studied in a purely Lagrangian and meshless approach, two-dimensional smoothed particle hydrodynamics (SPH) model. After the SPH model is calibrated with full-scale overtopping test results, the overtopping discharge, flow thickness, flow velocity, average overtopping velocity, shear stress, and soil erosion rate are calculated. New equations are developed for average overtopping discharge. The shear stresses on landward-side slope are calculated and the characteristics of soil loss are given. Equations are also provided to estimate soil loss rate. The range of the application of these equations is discussed.

Numerical Simulation of Tank Discharge Using Smoothed Particle Hydrodynamics

The study concerns the application of the smoothed particle hydrodynamics (SPH) method within computational fluid dynamics. In the present study, a tank discharge with a falling head is investigated. Water is modelled as a viscous fluid with weak compressibility. An enhanced treatment of the solid boundaries is used within the two-dimensional SPH scheme. The boundaries are represented by a special set of SPH particles that differ from the ones representing the fluid by being immovable, preventing the fluid from leaving the container. Particles with different colors are used to illustrate the sequence of the empting the tank as well as the velocity vectors to show stream lines. A code is developed using C++ to solve all equations explicitly by use of a Verlet algorithm. Results are compared to an analytical solution, and a good agreement is achieved.

Interaction of Submerged Breakwater by a Solitary Wave Using WC-SPH Method

Interaction of a solitary wave and submerged breakwater is studied in a meshless, Lagrangian approach. For this purpose, a two-dimensional smoothed particle hydrodynamics (SPH) code is developed. Furthermore, an extensive set of simulations is conducted. In the first step, the generated solitary wave is validated. Subsequently, the interaction of solitary wave and submerged breakwater is investigated thoroughly. Results of the interaction of solitary wave and a submerged breakwater are also shown to be in good agreement with published experimental studies. Afterwards, the effects of the inclination and length of breakwater as well as distance between two breakwaters are evaluated on damping ratio of breakwater.

Investigation of free surface flow generated by a planing flat plate using smoothed particle hydrodynamics method and FLOW3D simulations

In this article, smoothed particle hydrodynamics method is applied in order to study the free surface flow generated by two-dimensional planing flat plate. For this purpose, a two-dimensional smoothed particle hydrodynamics code is developed and validated by the well-known dam breaking problem. Four trim angles and three different velocities are considered to perform a parametric study to examine their physical effects. The obtained results from smoothed particle hydrodynamics are compared against the corresponding Reynolds-averaged Navier Stokes solutions. It is observed that at lower velocities, there exists a good agreement between the smoothed particle hydrodynamics and Reynolds-averaged Navier Stokes solutions, while at higher velocities, some inconsistency is observed. A brief discussion is presented to clarify the physical reasons behind the increase of the velocity and the height of the spray with the trim angle. Some formulas have also been derived to examine the variation of the ratio between the final wetted length of the flat plate and the initial wetted length at different velocities and trim angles.

Smoothed Particle Hydrodynamics Modeling of Combined Wave and Surge Overtopping and Hydraulic Erosion of an Articulated Concrete Block-Strengthened Levee System

Abstract Rao, X.; Li, L.; Amini, F., and Tang, H., 2012. Smoothed particle hydrodynamics modeling of combined wave and surge overtopping and hydraulic erosion of an articulated concrete block-strengthened levee system. Combined wave and surge overtopping may cause damage on earthen levees. Levee strengthened on the levee crest and landward-side slope can provide protection against the erosion damage induced by the combined wave and surge overtopping. In this paper combined wave overtopping and storm surge overflow of a levee with a trapezoidal cross section strengthened by an articulated concrete block (ACB) system was studied in a purely Lagrangian and meshless approach, two-dimensional smoothed particle hydrodynamics (SPH) model. By comparing with the results of full-scale experiment data, the model was verified, and the erosion parameters were calibrated. Time series of overtopping discharge and flow thickness at six locations on the levee crest and landward-side slope were calculated. New equations we...

An improved incompressible SPH model for simulation of wave–structure interaction

An improved two-dimensional Incompressible Smoothed Particle Hydrodynamics (ISPH) model is developed to simulate free surface flow interaction with structures. In this model, the improved mirror particle treatment for solid boundaries is developed, in which the mirror parameters and mirroring rules are redefined. The proposed mirror particle treatment is more accurate with less artificial oscillations of pressure. The improvement of pressure computations is verified by a benchmark test of dam break flow and the comparisons with the documented data showed satisfactory agreement. A series of numerical simulations have been conducted to further verify the applicability of the model for simulations of wave interaction with coastal structures of various shapes. These include linear wave reflection from an impermeable breakwater, solitary wave passing a rectangular obstacle and periodic wave train decompositions over a submerged shelf. In these simulations, the total particle number employed is up to 150,000 and rather good agreement has been obtained when the numerical results are compared to available analytical, experimental, and other numerical data found in literatures.