Incompressible Smoothed Particle Hydrodynamics Model Research Articles

Incompressible Smoothed Particle Hydrodynamics Simulation of Sediment Erosion around Submarine Pipelines

Sediment erosion around submarine pipelines is a popular topic, widely investigated in both ocean and submarine-pipeline engineering. In this paper, the incompressible smoothed-particle hydrodynamics (ISPH) method is modified for simulation of local scouring process around the submarine pipeline under the action of unidirectional flow. The erosion model is based on the Clear Water Particle–Turbid Water Particle–Critical Shear Stress (CWP-TWP-CSS) concept, and a sand–water two-phase model is proposed to deal with the sediment-entrained flow. The results of the numerical simulation are compared with the experimental data to verify the accuracy and applicability of the numerical model. The scouring process around the pipeline is investigated under different conditions, i.e., pipeline diameters, gap ratios, and flow velocities. The ISPH model is further used to study the flow characteristics of the scour pits around the submarine pipeline and the influence of the vortices on the maximum scour depth, to provide a theoretical basis for the stability design of submarine pipelines.

Extreme wave impacts on a suspended box above free surface

A systematic approach incorporating precision-controlled experiments and high-fidelity numerical simulations has been employed to delve deeper into the physics of extreme wave impact pressures. Using a suite of high-speed imaging and high-resolution pressure sensing techniques that are accurately synchronized with the wave generation, a consistent and well-correlated set of data providing details of the focusing incident wave front, flow velocities, and impact pressure time histories has been successfully obtained. The numerical simulations using a validated incompressible smoothed particle hydrodynamics (ISPH) provided further details that were not tractable in the experiments. Based on the results obtained, there were five broad impact scenarios identified, ranging from focusing crest impacts to plunging jet impacts with varying entrapped air. Among these impact types, the highest impact pressures were those associated with a focusing wave crest. It has been found that high impact pressures were correlated with a convergence of the horizontally impinging overturning crest and the vertical surge of the wall boundary water mass, but with the overturning crest impingement just ahead of the arrival of the wall boundary water mass, which in essence amounted to the impingement of a focusing wave front. Depending on the relative arrival times of the impinging crest and the wall boundary upsurge, the impact scenarios could vary from an up-slosh to a jet impingement with a clear entrapped air pocket, followed by a flip-through of the incident crest. For the scenario with the highest impact pressures, broadly classified as type II impact in this paper, the peak pressures could reach as high as 85ρC2, an order of magnitude higher than impact scenarios without the focusing effect, such as the scenario with a plunging jet impact with entrapped air (classified as types III and IV impact in this study). As the volume of entrapped air for this scenario was relatively small, the one-phase ISPH model used in this study was able to capture the peak pressure characteristics, including the peak pressure amplitudes. However, in scenarios with significantly highly entrapped air during impact, a two-phase model would be necessary.

A hybrid method combining ISPH with graph neural network for simulating free-surface flows

The incompressible Smoothed Particle Hydrodynamics (ISPH) is a popular Lagrangian Particle method. In the conventional ISPH method for simulating free-surface flows, the pressure-projection phase, which solves the pressure Poisson's equation (PPE), is the most time-consuming. In this paper, we propose a novel hybrid method by combining the graph neural network (GNN) with the ISPH for modelling the free-surface flows. In the new hybrid method, the graph neural network (GNN) is employed to replace solving the PPE for pressure in the conventional ISPH. To the best of knowledge of the authors, this is the first attempt to combine the GNN with ISPH model in a Lagrangian formulation. The performance of the hybrid method will be evaluated by comparing its results with experimental data, analytical solution or numerical results from other methods for three benchmark test cases: dam breaking, sloshing wave and solitary wave propagation. In addition, the potential of generalization of the hybrid method will be studied by applying it with the GNN model trained on data for relatively simple cases to simulate more complex cases. It will be demonstrated that the hybrid method does not only give satisfactory results, but also shows good potential of generalization. In addition, the new method will be demonstrated to require the computation time which can be 80 times less than the conventional ISPH for estimating pressure for cases with a large number of particles that is usually needed in the practical free-surface flows simulation using ISPH.

A CNN-supported Lagrangian ISPH model for free surface flow

As a popular method for modeling violent free surface flow, the incompressible Smoothed Particle Hydrodynamics (ISPH) based on the Lagrangian formulation has attracted a great attention worldwide. The Lagrangian ISPH solves the unsteady Navier-Stokes and continuity equations using the projection method, in which the pressure is obtained by solving the pressure Poisson's equation (PPE) that is the most time-consuming part in the ISPH procedure. In this paper, the Convolutional Neural Network (CNN) is combined with ISPH and used to predict the fluid pressure instead of solving the PPE directly. Although limited attempts of using CNN for solving the PPE in Eulerian formulation (referred to as the Eulerian CNN framework) in mesh-based methods are found in the public domain, the present model is the first ISPH model supported by CNN in a Lagrangian formulation. The proposed model overcome several challenges associated with combining CNN with ISPH, including selecting the input parameters, formulating the objective functions, producing the training dataset and dealing with boundary conditions. Two classic free surface problems, i.e. the dam breaking and the wave propagation, are simulated to evaluate the performance of the present model. Quantitative assessments of the numerical error in terms of both the free surface profile and the pressure field are carried out. The assessments show that the new model does not only give results with satisfactory accuracy, but also requires much less computation time for estimating pressure if the number of particles is large, e.g., 100 thousands particles that is usually required in the practical ISPH simulation for free surface flow.

An ISPH with modified k–ε closure for simulating breaking periodic waves

The Incompressible Smoothed Particle Hydrodynamics (ISPH) method, solving the 2D RANS (Reynolds Averaged Navier-Stokes) equations with the modified k–ε turbulence closure developed by Wang and Liu (2020) [ Coastal Engineering , 157, 1–28], is further extended to periodic waves. The capability of this numerical model is demonstrated by applying it to three laboratory experiments: (1) Dynamics of surf-zone turbulence generated by a spilling breaker and a plunging breaker over a plane slope in small-scale wave flume experiments, (2) breaking wave generated turbulence over a stationary barred beach in large-scale wave flume experiments, and (3) spatial and temporal distributions of turbulence generated by bi-chromatic breaking waves over a submerged stationary barred slope in medium-scale wave flume experiments. In this new ISPH model, the gradient correction_ dynamically stabilized scheme is adopted to reduce numerical dissipation. The experimental data for the spilling breaker on a plane beach is used to calibrate the model. Once the model is calibrated, all the empirical coefficients in the turbulence closure model, including the stress limiter coefficient λ 3 , which is required in modifying the eddy viscosity, are fixed for the validation processes with other experimental data sets. All model-data comparisons are made in terms of free surface profile, mean velocity field and turbulent kinetic energy. The differences between experimental observations and numerical simulations are quantified by the percentage error. Overall, good agreement is observed for all experiments. This paper presents the first comprehensively validated 2D ISPH model with the modified k–ε turbulence closure, which can be applied to periodic wave breaking problems. • The Incompressible Smoothed Particle Hydrodynamics (ISPH) method is coupled with the modified k–ε turbulence closure equations to solve the 2D RANS (Reynolds Averaged Navier-Stokes) equations. The gradient correction_ dynamically stabilized scheme is adopted to reduce numerical dissipation. • The model has been checked with three laboratory experiments for periodic breaking waves. (1) Spilling and plunging cnoidal waves over a plane slope in small-scale wave flume experiments, (2) plunging periodic breaking wave over a stationary barred beach in large-scale wave flume experiments, and (3) bi-chromatic breaking waves over a submerged stationary barred slope in medium-scale wave flume experiments. • All model-data comparisons are made in terms of free surface profile, mean velocity field and turbulent kinetic energy. • The differences between experimental observations and numerical simulations are quantified by the percentage error. • Overall, good agreement is observed for all experiments. Good agreements are observed in terms of free surface profile, mean velocity field, vorticity field, turbulent kinetic energy and turbulent shear stress.

Focused wave interaction with a partially-immersed rectangular box using 2-D incompressible SPH on a GPU comparing with experiment and linear theory

Wave interaction with bodies spanning the water surface is a common problem. A basic rectangular box of small draft is considered in two dimensions and focused waves are used to minimise reflections. Overtopping occurs in some cases making the inherently mass conservative smoothed particle hydrodynamics (SPH) method appropriate. This is applied in incompressible (divergence-free) form with a 2-D graphics processing unit (GPU) version of the Chow et al. (2019) code with some improvements. A newly parallelised GPU algorithm for the population of a compressed sparse row matrix storage array for the pressure Poisson equation is presented and provides a 327–446 times function speedup and overall simulation time speedups of 1.45–1.78 times with over 5 million particles. The inclusion of the parallel function leads to a completely parallel ISPH algorithm. Peak pressures on the base and front face are compared with experiment and linear (potential-flow) theory. The experiments used periodic focused waves which showed some variation in form about a peak crest although crest elevations were repeatable, and these are reproduced in the model. Converged incompressible SPH (ISPH) values are in approximate agreement with both. Overtopping of the box shows qualitative agreement with experiment. While linear theory cannot account for overtopping or viscous (eddy-shedding) effects, submerged pressure prediction provides a useful approximation. The ISPH model is single phase and limited video evidence suggests that air entrapment can occur in the initial stages of overtopping near the front face. Quite complex vorticity generation and eddy shedding is predicted with free-surface interaction. The study shows the capability and limitations of single phase ISPH for complex wave-body interaction.

Incompressible smoothed particle hydrodynamics model of a rectangular tuned liquid damper containing screens

Damping screens are often installed within a tuned liquid damper (TLD) to increase the energy dissipation beyond what the sloshing liquid alone can provide. Many numerical models exist to study the response of a TLD; however, there are often associated limitations on fluid depth or excitation amplitude. The smoothed particle hydrodynamics (SPH) method can capture the fully nonlinear TLD response without limitation by solving the Navier–Stokes equations throughout the fluid domain. A two-dimensional explicit incompressible SPH model is presented and validated against a hydrostatic and dam break flow scenario. The damping screens are modelled in SPH on a macroscopic level using Morison’s equation for force on an object submerged in fluid flow. This implementation is computationally efficient compared to explicitly modelling the damping screens using solid particles as it allows for a much larger initial particle spacing. The SPH model results for screen forces, wave heights, and TLD sloshing water forces are validated against experimental time and frequency response data. The SPH model is found to be in excellent agreement with the experimental data for a range of TLD tank dimensions (L=0.966 and 1.524 m), fluid depths (h/L= 0.05 to 0.25), excitation amplitudes (X0/L= 0.0025 to 0.031), and excitation frequencies (β=0.7 to 1.3). The presented SPH model for a TLD with damping screens can be used to study the nonlinear response of a rectangular TLD.

An ISPH with k–ε closure for simulating turbulence under solitary waves

In this paper an Incompressible Smoothed Particle Hydrodynamics (ISPH) method solving the 2D RANS (Reynolds Averaged Navier-Stokes) equations with the k–ε turbulence closure is constructed. In the present model, the concept of “massless ISPH” utilizing the definition of “particle density” (number of computational particles within unit volume) is stressed. The skills of this numerical model are tested by applying to two laboratory experiments: (1) A non-breaking solitary wave propagating over a bottom-mounted barrier and (2) a solitary wave breaking on a 1 on 50 slope. In the former case flow separation occurs behind the barrier as the wave crest passes by and a vortex is generated, which later interacts with free surface causing breaking. In the latter case wave breaking and bottom friction both generate significant turbulence. For both cases, the effects of initial seeding of turbulent kinetic energy, required in the k–ε model, are studied and it is concluded that initial values of O (10−10) to O (10−8) m2/s2 should be used. An adaptive wall boundary condition for k–ε turbulence model is employed to avoid the unrealistic production of turbulence near the wall boundary. The numerical results, in terms of free surface profile, mean velocity field, vorticity field, turbulent kinetic energy and turbulent shear stress, are compared with experimental data. Very reasonable agreement is observed. This paper presents the first comprehensively validated 2D ISPH model with the k–ε turbulence closure, which can be applied to transient free surface wave problems.

Interactive fluid flow simulation in computer graphics using incompressible smoothed particle hydrodynamics

AbstractInteractive simulations of fluids flow play an important role in several computer graphics‐based applications such as computer games, computer animation, movie industry, and virtual realities. The incompressible smoothed particle hydrodynamics (ISPH) model is a promising numerical scheme for large‐scale and large‐deformation simulations, where the pressure can be determined precisely by solving pressure Poisson equation (PPE). The three main shortcomings of the ISPH scheme are oscillating pressure, particles disorders, and particles penetrations through rigid boundary. In this paper, the stable pressure is obtained from modifications in the source term of PPE, in which the divergence‐free velocity condition plus density‐invariance condition multiply by a relaxation coefficient are included. The particles disorders are solved via utilizing a shifting technique with the current treatment of source term in PPE. Additionally, the dummy boundary particles are used for the rigid boundary treatment. For getting enough pressure on the boundary, the Neumann boundary condition is satisfied during the implicit solving processes. The performance of the stabilized ISPH model is tested on various numerical simulations with largely distorted free surface including liquid sloshing problems, fluid–fluid and fluid–structure interactions, and dam‐break flows. To extend the applicability of the stabilized ISPH model, the post process including visual realism with a highly rendering scheme is coupled. The coupled scheme introduces several simulations including free falling of a rigid body, water splashes, and dam break analysis. Furthermore, the proposed ISPH‐based method enables efficient and viscous fluid simulations with large time steps, higher viscosities, and resolutions, and it is a robust scheme in long interval simulations of nonlinear free‐surface flows.

A numerical study of tuned liquid damper based on incompressible SPH method combined with TMD analogy

Tuned liquid dampers (TLDs) are economical dynamic vibration absorbers which are increasingly being used for structural response control. Nevertheless, a thorough understanding of the sloshing behavior inside the TLD is essential for efficient design. In this paper, a truly incompressible smoothed particle hydrodynamics (ISPH) method is employed to circumvent the difficulties regarding the simulation of fully nonlinear sloshing motion induced by large amplitude excitations. The behavior of the TLD with damping screens is studied numerically over a wide range of excitation frequencies and amplitudes. It is found through comparison with the existing experimental data that the ISPH model is a powerful tool for accurate predictions of the TLD behavior. The amplitude-dependent properties of an equivalent tuned mass damper (TMD) model, which is capable of reproducing the energy dissipation characteristics of the TLD, are derived from the simulations results. Good agreement between the numerical and experimental results is indicative of the equivalent model’s ability to predict the response of structure–TLD systems, suggesting that the ISPH model can properly simulate the TLD behavior. The effect of screen placement on the performance of structure–TLD systems is also investigated. Findings reveal that improved performance of TLD can be realized under high amplitude excitations by placing the damping screens in the locations corresponding to the higher sloshing modes.

Coupled incompressible Smoothed Particle Hydrodynamics model for continuum-based modelling sediment transport

A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.

2D Numerical ISPH Wave Tank for Complex Fluid–Structure Coupling Problems

In this paper, we provide a hybrid incompressible Smoothed Particle Hydrodynamics (ISPH) model for fluid-structure interactions. The numerical algorithms include the mirroring treatment of solid boundary, free surface tracking, wave damping using sponge layer and fluid-solid coupling model. The proposed ISPH wave tank is applied to a series of wave-structure coupling problems including the sloshing in a baffled tank, solitary wave impact on an underwater obstacle, water entry of a cylinder and balance dynamics of a floating object. The simulation results demonstrate that the ISPH model provides an accurate simulation technique in various fluid-structure coupling studies.

Three-Gorges Dam Fine Sediment Pollutant Transport: Turbulence SPH Model Simulation of Multi-Fluid Flows

The Three Gorges Dam (TGD) constructed at the Yangtze River, China represents a revolutionary project to battle against the mage-scale flooding problems while improving the local economy at the same time. However, the large-scale fine-size sediment and pollutant material transport caused by the TGD operation are found to be inevitable and long-lasting. In this paper, a multi-fluid Incompressible Smoothed Particle Hydrodynamics (ISPH) model is used to simulate the multi-fluid flows similar to the fine sediment materials transport (in muddy flows) and water flow mixing process. The SPH method is a mesh-free particle modeling approach that can treat the free surfaces and multi-interfaces in a straightforward manner. The proposed model is based on the universal multi-fluid flow equations and a unified pressure equation is used to account for the interaction arising from the different fluid components. A Sub-Particle-Scale (SPS) turbulence model is included to address the turbulence effect generated during the flow process. The proposed model is used to investigate two cases of multi-fluid flows generated from the polluted flow intrusions into another fluid. The computations are found in good agreement with the practical situations. Sensitivity studies have also been carried out to evaluate the particle spatial resolution and turbulence modeling on the flow simulations. The proposed ISPH model could provide a promising tool to study the practical multi-fluid flows in the TGD operation environment.

Incompressible SPH simulation of wave interaction with porous structure

In this paper an incompressible Smoothed Particle Hydrodynamics (ISPH) method is applied to investigate the flow motion in and around the porous structure. In order to describe in a simple and effective way the flow through the interface between the porous region and pure fluid region within the SPH framework, a heuristic boundary treatment method has been proposed. The ISPH model is first verified against a theoretical model of wave propagation over a porous bed and then further validated by comparing the predicted wave surface profiles and flow velocity fields with the experiment data for a typical case of flow motion around and inside a submerged porous structure. The good agreement has demonstrated that the improved ISPH model developed in this work is capable of modelling wave interaction with porous structures.

Incompressible SPH simulation of open channel flow over smooth bed

The Smoothed Particle Hydrodynamics (SPH) modelling techniques are used in a variety of coastal hydrodynamic applications, but only limited works have been documented in the open channel flows. In this paper, we use the incompressible SPH model combined with an improved inflow boundary scheme to investigate the open channel flows in a laboratory scale. The inflow and outflow boundary conditions are treated by generating and removing the fluid particles at the channel end. The proposed ISPH model has been applied to the open channel laminar and turbulent flows of different flow depths and the computational results have been verified against the analytical solutions. Model convergence has been investigated through the numerical tests using different particle spacings and time steps. The artificial boundary drag force of numerical nature has been found under certain flow conditions. As further application of the model, two additional tests are also carried out, involving alternative solid boundary treatment and more complex channel topography. The present study could provide useful information on further exploitation of the SPH modelling technique in river hydrodynamics.

Incompressible SPH scour model for movable bed dam break flows

In this study an incompressible smoothed particle hydrodynamics (ISPH) approach coupled with the sediment erosion model is developed to investigate the sediment bed scour and grain movement under the dam break flows. Two-phase formulations are used in the ISPH numerical algorithms to examine the free surface and bed evolution profiles, in which the entrained sediments are treated as a different fluid component as compared with the water. The sediment bed erosion model is based on the concept of pick-up flow velocity and the sediment is initiated when the local flow velocity exceeds a critical value. The proposed model is used to reproduce the sediment erosion and follow-on entrainment process under an instantaneous dam break flow and the results are compared with those from the weakly compressible moving particle semi-implicit (WCMPS) method as well as the experimental data. It has been demonstrated that the two-phase ISPH model performed well with the experimental data. The study shows that the ISPH modelling approach can accurately predict the dynamic sediment scouring process without the need to use empirical sediment transport formulas.

Buoyancy modelling with incompressible SPH for laminar and turbulent flows

SummaryThis work aims to model buoyant, laminar or turbulent flows, using a two‐dimensional incompressible smoothed particle hydrodynamics model with accurate wall boundary conditions. The buoyancy effects are modelled through the Boussinesq approximation coupled to a heat equation, which makes it possible to apply an incompressible algorithm to compute the pressure field from a Poisson equation. Based on our previous work [1], we extend the unified semi‐analytical wall boundary conditions to the present model. The latter is also combined to a Reynolds‐averaged Navier–Stokes approach to treat turbulent flows. The k − ϵ turbulence model is used, where buoyancy is modelled through an additional term in the k − ϵ equations like in mesh‐based methods. We propose a unified framework to prescribe isothermal (Dirichlet) or to impose heat flux (Neumann) wall boundary conditions in incompressible smoothed particle hydrodynamics. To illustrate this, a theoretical case is presented (laminar heated Poiseuille flow), where excellent agreement with the theoretical solution is obtained. Several benchmark cases are then proposed: a lock‐exchange flow, two laminar and one turbulent flow in differentially heated cavities, and finally a turbulent heated Poiseuille flow. Comparisons are provided with a finite volume approach using an open‐source industrial code. Copyright © 2015 John Wiley & Sons, Ltd.

INCOMPRESSIBLE SMOOTHED PARTICLE HYDRODYNAMICS (ISPH) MODELLING OF BREAKWATER OVERTOPPING

This paper describes an investigation into using incompressible smoothed particle hydrodynamics (ISPH) to simulate the overtopping of a coastal structure such as a breakwater. The paper presents the ISPH formulation that employs the multiple boundary tangent method and the latest developments such as particle shifting that produce noise-free pressure fields. The numerical model is compared with experimental overtopping data for a solitary wave and a crest-focussed wave group approaching a trapezoidal breakwater. The ISPH model is shown to produce close agreement for the free-surface evolution for both types of wave and generates overtopping volumes in satisfactory agreement with experimental data. Closer agreement with experimental data is obtained for ISPH compared to more popular weakly compressible SPH for the same resolution or particle size. Future work identifies conducting a convergence study and using more sophisticated boundary treatments.

Incompressible smoothed particle hydrodynamics modeling of thermal convection

An incompressible smoothed particle hydrodynamics (ISPH) method based on the incremental pressure projection method is developed in this study. The Rayleigh-Benard convection in a square enclosure is used as a validation case and the results obtained by the proposed ISPH model are compared to the benchmark solutions. The comparison shows that the established ISPH method has a good performance in terms of accuracy. Subsequently, the proposed ISPH method is employed to simulate natural convection from a heated cylinder in a square enclosure. It shows that the predictions obtained by the ISPH method are in good agreements with the results obtained by previous studies using alternative numerical methods. A rotating and heated cylinder is also considered to study the effect of the rotation on the heat transfer process in the enclosure space. The numerical results show that for a square enclosure at , the addition of kinetic energy in the form of rotation does not enhance the heat transfer process. The method is also applied to simulate forced convection from a circular cylinder in an unbounded uniform flow. In terms of results, it turns out that the proposed ISPH model is capable to simulate heat transfer problems with the complex and moving boundaries.

Simulation of 2-D Dam Break Using Improved Incompressible Smoothed Particle Hydrodynamics Based on Projection Method

This paper deals with numerical modeling of water flow which is generated by the break of a dam. The problem is solved by applying a new Incompressible Smoothed Particle Hydrodynamics (ISPH) algorithm based on projection method. The proposed ISPH model has two steps. In the first step, the incompressibility of fluid is maintained regarding to the changes of intermediate and initial particles densities at the first half-time step (stability step). In the second step, by computing the divergence of the intermediate secondary velocity at the second half-time step (accuracy step), the incompressibility is satisfied completely. In fact, by using this method both stability and accuracy are increased. The simulation illustrates the formation and subsequent propagation of a wave over the horizontal plane. It is shown that the model predictions compare well with experimental data.