Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> The SPH (smoothed particle hydrodynamics) method is extended to deal with free surface incompressible flows. The method is easy to use, and examples will be given of its application to a breaking dam, a bore, the simulation of a wave maker, and the propagation of waves towards a beach. Arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles. The method is explicit, and the time steps are therefore much shorter than required by other less flexible methods, but it is robust and easy to program. <s> BIB001 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> An implementation of the smoothed particle hydrodynamics (SPH) method is presented to treat two-dimensional interfacial flows, that is, flow fields with different fluids separated by sharp interfaces. Test cases are presented to show that the present formulation remains stable for low density ratios. In particular, results are compared with those obtained by other solution techniques, showing a good agreement. The classical dam-break problem is studied by the present two-phase approach and the effects of density-ratio variations are discussed. The role of air entrapment on loads is discussed. <s> BIB002 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> The impact of a single wave generated by a dam break with a tall structure is modeled with a three-dimensional version of the smoothed particle hydrodynamics method. The method is used to analyze the propagation of a long wave and the force it exerts on a tall structure located in a region with vertical boundaries. Velocities and forces obtained from a numerical model are shown to be in good agreement with laboratory measurements. The effect of having a dry bed in front of the dam prior to the dam break versus a wet bed in the experiment is discussed. <s> BIB003 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> We describe the work performed in the numerical simulation of passive roll-damper tanks for fishing vessels. The fluid in the tank behaves as a resonant fluid system, and this resonant behavior justifies their usage as counter-moment generators for sea waves. Although the experimental data come from the naval field, the techniques may be applied to design other tuned liquid damper and tuned sloshing damper devices. The differences with respect to other techniques arise from using the smoothed particle hydrodynamics (SPH) method to perform simulations. With SPH, it is feasible to model large free surface deformations and wave breaking. The results of the simulations have been validated with experimental tests corresponding to real configurations. Against experimental data, we compare pure quantitative physical magnitudes as moment phase lags with respect to tank movement and more qualitative ones as free surface shapes. Although large amplitude waves and breaking waves appear, they are well reproduced and the numerical values of phase lags accord to the experiments. To summarize, the results are promising but further work has yet to be done. <s> BIB004 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> The paper presents an incompressible Smoothed Particle Hydrodynamics (SPH) model to investigate the wave overtopping of coastal structures. The SPH method is a grid-less Lagrangian approach which is capable of tracking the large deformations of the free surface with good accuracy. The incompressible algorithm of the model is implemented by enforcing the constant particle density in the pressure projection. The SPH model is employed to reproduce a transient wave overtopping over a fixed horizontal deck and the regular/irregular waves overtopping of a sloping seawall. The computations are validated against the experimental and numerical data and a good agreement is observed. The SPH modelling is shown to provide a promising tool to predict the overtopping characteristics of different waves. The present model is expected to be of practical purpose if further improvement in the spatial resolution and CPU time can be adequately made. <s> BIB005 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> Abstract Smoothed Particle Hydrodynamics (SPH) is a relatively new method for examining the propagation of highly nonlinear and breaking waves. At Johns Hopkins University, we have been working since 2000 to develop an engineering tool using this technique. However, there have been some difficulties in taking the model from examples using a small number of particles to more elaborate and better resolved cases. Several improvements that we have implemented are presented here to handle turbulence, the fluid viscosity and density, and a different time-stepping algorithm is used. The final model is shown to be able to model breaking waves on beaches in two and three dimensions, green water overtopping of decks, and wave–structure interaction. <s> BIB006 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> We present a novel, incompressible fluid simulation method based on the Lagrangian Smoothed Particle Hydrodynamics (SPH) model. In our method, incompressibility is enforced by using a prediction-correction scheme to determine the particle pressures. For this, the information about density fluctuations is actively propagated through the fluid and pressure values are updated until the targeted density is satisfied. With this approach, we avoid the computational expenses of solving a pressure Poisson equation, while still being able to use large time steps in the simulation. The achieved results show that our predictive-corrective incompressible SPH (PCISPH) method clearly outperforms the commonly used weakly compressible SPH (WCSPH) model by more than an order of magnitude while the computations are in good agreement with the WCSPH results. <s> BIB007 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> In this paper, sloshing phenomenon in a rectangular tank under a sway excitation is studied numerically and experimentally. Although considerable advances have occurred in the development of numerical and experimental techniques for studying liquid sloshing, discrepancies exist between these techniques, particularly in predicting time history of impact pressure. The aim of this paper is to study the sloshing phenomenon experimentally and numerically using the Smoothed Particle Hydrodynamics method. The algorithm is enhanced for accurately calculating impact load in sloshing flow. Experiments were conducted on a 1:30 scaled two-dimensional tank, undergoing translational motion along its longitudinal axis. Two different sloshing flows corresponding to the ratio of exciting frequency to natural frequency were studied. The numerical and experimental results are compared for both global and local parameters and show very good agreement. <s> BIB008 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> Smoothed particle hydrodynamics (SPH) is a popular meshfree, Lagrangian particle method with attractive features in modeling liquid sloshing dynamics, which is usually associated with changing and breakup of free surfaces, strong turbulence and vortex, and ''violent'' fluid-solid interaction. This paper presents an improved SPH method for modeling liquid sloshing dynamics. Firstly, modified schemes for approximating density (density correction) and kernel gradient (kernel gradient correction, or KGC) have been used to achieve better accuracy with smoother pressure field. Secondly, the Reynolds Averaged turbulence model is incorporated into the SPH method to describe the turbulence effects. Thirdly, a coupled dynamic solid boundary treatment (SBT) algorithm has been proposed to improve the accuracy near the solid boundary areas. The new SBT algorithm consists of a kernel-like, soft repulsive force between approaching fluid and solid particles, and a reliable numerical approximation scheme for estimating field functions of virtual solid particles. Three numerical examples are modeled using this improved SPH method, and the obtained numerical results agree well with experimental observations and results from other sources. <s> BIB009 </s> Survey on Smoothed Particle Hydrodynamics and the Particle Systems <s> B. FREE SURFACE FLOW <s> The first author acknowledges the Jafar Studentship for her PhD study at University of Cambridge. We thank the Open Research Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (SKHL1404; SKHL1409). <s> BIB010
Vertical pressure of free surface flow transits continuously and smoothly to zero, but there exists a discontinuous sudden change of density from fluid density to zero below the surface. The boundary conditions on arbitrarily moving surface are special. At present, MAC and VOF methods are ideal methods to deal with this situation, but both of them have numerical diffusion problems caused by convection term in N -S equation. Because of its Lagrangian characteristics, SPH method solves this problem well and is especially suitable for the simulation of free interface flow. Dam break simulation is one of the earliest applications of SPH in hydrodynamics. The dam break is a type of wave motion simulation problem. In 1994, J. J. Monaghan first created a model for simulating incompressible fluids by simulating dam break problems BIB001 . Thereafter, many scholars on this issue have sought in-depth studies. Shao et al. BIB005 studied the dam break problem, combined with a large eddy simulation, and discussed the climbing of isolated waves. Colagross and Landrini BIB002 modeled the flow of water against an upright wall by setting up an upright wall downstream. Gesteira and Dalrymple BIB003 used WCSPH to simulate the movement of dam-break water flow and analyzed the impact of dam-breakwater waves on high-rise buildings and wave breaking. Jian et al. BIB010 used WCSPH and ISPH to simulate the collision process between dam breakwater flow and moving and fixed obstacles. Figure 9 shows the use of WCSPH to simulate a dam break scenario at different times. The SPH simulations of incompressible flows are mainly classified as weak compressible models (WCSPH) and strict incompressible models (ISPH). The actual fluid is compressible, and the incompressible fluid is an idealized mechanical model. The liquid compression coefficient is very small, and the density is almost constant in the range of considerable pressure changes. Therefore, the liquid balance and the motion problem all treat the liquid as an incompressible fluid for theoretical analysis. The gas compressibility is much larger than that of the liquid. In all natural atmospheric movements, air velocity is small; it is much smaller than the speed of sound. The flow process density did not change significantly and can still be used as incompressible fluid treatment. For the simulation of incompressible flow in the dam, wave motion, river hydrodynamics, and multiphase flow and its interaction with other structures have been developed by leaps and bounds. WCSPH establishes the relational expression of the density error and the pressure using the Tait equation, ensuring the incompressibility of the fluid by using large stiffness coefficients to control the error. When simulating by ISPH, the pressure of the particle is obtained by the discrete pressure Poisson formula, allowing for a large time step and becoming a common method in computational fluid dynamics and computer graphics. Although the WCSPH and ISPH can be used to impose incompressibility, they have low computational efficiency. In response to this problem, Solenthaler and Pajarola BIB007 proposed the PCISPH method, which uses split ideas to split the forces on the particles into pressure and other forces, eliminating the limitations of the time step such that it can be used for interactive real-time simulation. Free surface flow problems are also widespread in the ship, aerospace, water conservancy, civil engineering, and other fields. SPH is also suitable for ship hydrodynamics. The study of ship hydrodynamics mainly includes hull resistance, tank sloshing, and overturning. In the sloshing problem, SPH gradually became one of the main tools in the numerical analysis of the problem. Iglesias et al. used SPH to study the problem of the moment amplitude in the sloshing. Iglesias et al. BIB004 studied the sloshing problem of damping tanks Shao et al. BIB009 used the improved fixed boundary condition to study the sloshing problem. Rafiee et al. BIB008 used the threedimensional SPH model to study the problem of sloshing and obtained results and compared them with the experimental findings. Turbulence simulation has always been a hot topic in SPH method.. Dalrymple and Rogers BIB006 improved the SPH algorithm to handle turbulence, the fluid viscosity and density, and a different time stepping. The model is shown to be able to model breaking waves on beaches in two and three dimensions, green water overtopping of decks, and wavestructure interaction.