Search

In this work, a robust corrected weakly compressible smoothed particle hydrodynamics scheme combined with several improved interface treatments (CWCSPH-IT) is proposed to investigate viscous or viscoelastic two-phase flows of high density ratios. The proposed viscoelastic two-phase CWCSPH-IT model is mainly derived from three aspects: (a) a combined elastic stress approximation in the momentum equation based on the weighted idea is proposed; (b) the transition region near the interface of two fluids is regarded as a weak polymer fluid by approximating the relaxation time with a Shepard interpolation which handles the discontinuity of elastic stress near the interface; and (c) a new mixed boundary treatment is proposed to treat the wall boundary in a viscoelastic flow. Moreover, a weighted color gradient scheme is adopted to handle the surface tension near the phase interface, and a particle shifting technique is used to regularize particle distributions and enhance numerical stability. Several two-phase benchmark problems are simulated to test the validity and reliability of the proposed CWCSPH-IT. Subsequently, the proposed particle scheme is adopted to simulate the droplet rising in viscous/viscoelastic matrix fluid with high density ratios. Further, the stable dimple shape of a polymer drop falling in a low-density matrix, and the complex overshooting, oscillation and breakup phenomena of a drop in a high-viscoelasticity shear fluid are numerically investigated. The comparison between the SPH and other reliable reference results demonstrates the ability of the present viscoelastic two-phase scheme in modeling complex viscous or viscoelastic multi-phase problems.

Floating breakwaters have better performance than fixed breakwaters in deep water conditions owing to their higher durability and lower cost. To evaluate the hydrodynamics of a floating breakwater system, a coupling model between smoothed particle hydrodynamics and a multisegmented quasi-Static method is developed. The free-floating and the moored cases are firstly employed as benchmarks to validate the accuracy and stability of the proposed numerical procedure. The coupling model is then utilized to investigate the wave-attenuating performance of a novel configuration of floating breakwater under different environmental conditions. It is demonstrated that the induced response and the tension characteristics are both in good agreement with experimental results, which means that the developed coupling model is capable of predicting the hydrodynamics of the floating breakwater system. Moreover, it is also suggested that the newly-proposed configuration shows more satisfactory wave-attenuating performance than the classical type by inducing more complex velocity fields surrounding the breakwater.

Spurious pressure and density waves often occur in weakly-compressible SPH simulations and their propagation and reflection from the boundaries generally lead to large oscillations in the pressure field and noise in the measured loads on solid structures. In the present work this problem is tackled by adding an artificial damping term for acoustic waves in the momentum equation, as theoretically proposed in [1]. Similarly to other diffusive terms previously proposed for weakly-compressible SPH schemes, the present acoustic damper term converges to zero when the particle resolution increases, proving to be numerically consistent. Numerical results show that the acoustic damper is effective in removing the spurious acoustic noise.

This paper aims at presenting a general-purpose-oriented and fully parallelized meshless framework to simulate complex Fluid–Structure Interaction (FSI) problems in ocean engineering. In this framework, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) solver is combined with several advanced pre- and post-processing techniques. Based on the framework, we have been developing our in-house WCSPH-FSI package named SPHydro for solving hydrodynamic problems involving complex FSI processes in an accurate, efficient, and convenient manner. Three benchmarks are performed to qualitatively and quantitatively validate the accuracy and convergence of SPHydro. In addition, several practical applications are also provided to further highlight the generality and applicability of SPHydro in ocean engineering simulations. It is demonstrated that SPHydro holds satisfactory performance in solving complex FSI problems in ocean engineering and that the present framework can be further developed to tackle more complex FSI problems for general engineering applications due to its high flexibility and extensibility.

In this paper, the Lagrangian particle method δ - P l u s -SPH model is used to solve a series of benchmark test-cases of vortex induced vibrations (VIV). An Adaptive Particle Refinement (APR) technique is adopted to resolve correctly the boundary layer regions of the moving bodies, and to de-refine the particles that are transported far away. Furthermore, a switch correction on the pressure forces term is adopted in the momentum equation to completely remove the occurrence of the so-called Tensile Instability that leads to the development of numerical cavitation in negative pressure regions. Because of the Lagrangian nature of the method, difficulties arise when intense vortex wakes, typically developed in VIV problems, cross the outflow boundary. To this purpose, a damping zone is also implemented close to the outlet to improve the numerical stability of the scheme. The fluid–structure coupling technique is based on ghost particles properly generated inside the solid bodies. The validation is performed against test-cases for which reference solutions are available in the literature. Within those test-cases challenging benchmarks involving small mass ratios, large-amplitude body motions and multi-body interactions have been selected. For all the benchmark test-cases the δ - P l u s -SPH results are in good agreement with the reference solutions, demonstrating the ability of this particle method in solving complex VIV problems.

In this paper, a weakly compressible updated Lagrangian particle hydrodynamics (ULPH) model [1] has been developed for multiphase flows with high density ratios and viscosity ratios. To enhance computation stability and prevent penetrations near the multiphase flow interface, a new surface tension resultant formulation based on the Continuum Surface Force (CSF) formulation [2] , combined with the interface sharpness force, is also developed within the framework of ULPH method. The intermediate configuration is considered in the computational algorithm, and a modified predictor-corrector scheme is adopted to solve governing equations, which significantly improve the accuracy and efficiency of the ULPH model. Several numerical examples are presented to compare with either analytical or computational results obtained by using different numerical methods such as Smoothed Particle Hydrodynamics (SPH) method, Moving Particle Semi-implicit (MPS) method and Level Set (LS) method within the framework of Finite Element Method (FEM). The results indicate that the ULPH method has good accuracy, stability, and convergence properties in simulations of multiphase flows.

In the present work a consistent inclusion of a particle shifting technique (PST) in the weakly compressible Smoothed Particle Hydrodynamic (SPH) models is discussed. Recently, it has been shown that the use of PST can largely improve both the accuracy and the robustness of SPH models. In particular, the δ + -SPH model is a weakly-compressible SPH model where a PST is adopted along with a diffusive term in the continuity equation that helps removing the high-frequency noise on the pressure field. This specific SPH model is able to overcome the main drawbacks that afflict the standard weakly-compressible SPH model. In this work we demonstrate that a consistent introduction of the PST inside the SPH model leads to a new set of equations where some additional terms containing the particle shifting velocity δ u have to be taken into account. The effects of these δ u -terms become crucial for problems in confined or periodic domains, as well as for long-time simulations of free-surface flows. The proposed scheme is tested against challenging benchmark cases, highlighting when the δ u -terms play an important role or not. Further improvements of the PST algorithms for the numerical treatment of the scheme close to the free surface and along the solid boundaries are also discussed.

Compared to the case in still water, a damaged ship flooding in waves can be more complex with more violent shaking and accompanied by wave breaking and splashing. Therefore, in this work, a numerical study regarding the damaged ship cabin flooding in transversal regular waves is carried out based on a weakly compressible Smoothed Particle Hydrodynamics (WCSPH) method. Firstly, the governing equation, the fluid-structure interface treatment, the non-reflection sponge layer boundary and the information extraction of particle flow field are discussed respectively. Then, the numerical method is validated from two aspects: the experiment of a damaged ship cabin flooding is carried out to test the accuracy of the fluid-structure interaction model and a standard example is employed to validate the regular wave model. Furthermore, the influences of transversal regular waves on the flooding of a damaged ship cabin are explored. The openings at the broadside away from and towards the incident wave are considered. The six-degree-of-freedom (6-DOF) responses of the ship body to the incident waves are focused. This study can provide references for the hydrodynamic performance of damaged ships and decision makings of the rescue after marine accident.

This paper presents an improved particle shifting technology (IPST) for smoothed particle hydrodynamics (SPH). It allows particles in the vicinity of the free-surface to be shifted in all the directions in case they are not uniformly distributed, rather than just shifted tangentially to the free-surface in some conventional particle shifting technologies. Therefore, with the new technique, the imprecise shifting due to the inaccurate evaluations of the local normal and tangential vectors of the free-surface can be avoided, and a more uniform particle distribution near the free-surface can be obtained even for long-term simulations, which improves the accuracy and stability of the SPH method. Besides, by combining the advantages of two existing free-surface detection methods, an optimized detection approach is provided. It is capable of detecting the free-surface particles accurately, and meanwhile, it is easier to implement and requires lower computational costs, especially for three-dimensional problems. Several numerical tests show that the proposed IPST and the optimized free-surface detection method are robust and accurate for the simulation of a variety of free-surface flows.

The present work is dedicated to the enhancement and application of the recently developed delta(+)-SPH scheme for two and three dimensional water entry problems. The cylinder surface presents a circular shape and therefore the position where the flow separation happens is tightly related to the implementation of the boundary condition. A special treatment for the particle shifting between fluid and solid wall is highlighted. Adaptive particle refinement (APR) is applied in this work to reduce the computational cost. It is found that, APR and the delta(+)-SPH scheme benefit to each other. That is to say the former reduces the computing cost of the latter while in return the latter solves the problem of particle disorder of the inactive particles of the former. Thanks to the combination of APR and delta(+)-SPH especially in three dimensional (3D) cases, the overall computational cost is significantly reduced while sufficiently fine particle resolution can be obtained in the flow region characterized by large pressure gradient close to the structure surface. The fairly good agreements between the SPH results and the experimental data prove the present SPH model to be a reliable tool in accurately solving the fluid-structure interacting problems in ocean engineering. (C) 2018 Elsevier Ltd. All rights reserved.

Smoothed particle hydrodynamics (SPH) method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse (mother) particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process, conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.

This paper is dedicated to (1) emphasizing the importance of removing the Tensile Instability (TI) induced by negative pressures in Smoothed Particle Hydrodynamics (SPH) simulations, and (2) proposing new modifications for the Tensile Instability Control (TIC) and Particle Shifting Technique (PST) to simulate Fluid–Structure Interaction (FSI) phenomena with violent free-surface evolutions. Four numerical benchmarks associated with classical FSI problems characterized by negative pressures are simulated to show how the tensile instability destroys an SPH simulation without any TI prevention strategies. Therefore, PST and TIC are adopted into the SPH simulations for the sake of suppressing the tensile instability. However, different combinations of TI prevention strategies, i.e. different combinations of PST and TIC, lead to different results, and hence detailed investigations and discussions are provided. It is demonstrated that when negative pressures are moderate, solely using either PST or TIC works well. Nonetheless, it is in favor of using both PST and TIC if an SPH simulation is characterized by extremely strong negative pressures. Furthermore, for the problems with a convex-shaped structure penetrating a free-surface, special modifications are necessary for both PST and TIC in order to obtain accurate SPH results.

Bodies penetrating fluid interfaces is a classical issue that has been considerably investigated, especially for water entry problems, because of its relevance to slamming phenomena in ocean and coastal engineering. This paper is dedicated to investigating the water entry problems of a wedge characterized by different density-ratios using multi-phase Smoothed Particle Hydrodynamics (SPH) simulations. The SPH model is combined with an Adaptive Particle Refinement (APR) incorporating with a phase-switch correction to improve the numerical accuracy and computational efficiency of simulations. Firstly, an SPH simulation for a classical water entry process of a wedge is employed as a benchmark to validate the accuracy and stability of the utilized SPH model. Subsequently, the mechanisms of the spatiotemporal cavity behaviors for different density-ratios are simulated and discussed in detail. It is demonstrated that the cavity evolutions during penetrating and motion characteristics of the wedge are significantly affected by density-ratios. It is also suggested that the presented multi-phase SPH model with APR can be treated as a reliable numerical tool for solving such problems in terms of complex fluid interfaces behind moving structures.

With the quasi-static analysis method, the terminal floating state of a damaged ship is usually evaluated for the risk assessment. But this is not enough since the ship has the possibility to lose its stability during the transient flooding process. Therefore, an enhanced smoothed particle hydrodynamics (SPH) model is applied in this paper to investigate the response of a simplified cabin model under the condition of the transient water flooding. The enhanced SPH model is presented firstly including the governing equations, the diffusive terms, the boundary implementations and then an algorithm regarding the coupling motions of six degrees of freedom (6-DOF) between the structure and the fluid is described. In the numerical results, a non-damaged cabin floating under the rest condition is simulated. It is shown that a stable floating state can be reached and maintained by using the present SPH scheme. After that, three-dimensional (3-D) test cases of the damaged cabin with a hole at different locations are simulated. A series of model tests are also carried out for the validation. Fairly good agreements are achieved between the numerical results and the experimental data. Relevant conclusions are drawn with respect to the mechanism of the responses of the damaged cabin model under water flooding conditions.

The present work is dedicated to the improvement of the δ -SPH scheme. This is an enhanced weakly-compressible SPH model widely used in recent years thanks to its benefits to the standard SPH scheme, to its low CPU costs and to its ease of implementation. Nonetheless, the δ -SPH still presents some drawbacks as other SPH models. For example, in some critical conditions it does not prevent the tensile instability and the consequent numerical fragmentation. Furthermore, even if the use of a diffusive term in the SPH continuity equation is able to reduce numerical high frequencies on the pressure field, the velocity gradients are generally noisy because of the irregularities of the particle spatial configurations , which, in specific flow conditions, can induce also extra numerical-dissipation. For these reasons a particle shifting technique is used to improve the model and a special treatment has been developed for particles that are close to the free-surface region. The introduction of the particle-shifting procedure is generalized in the context of multi-resolutions for which a novel algorithm is formulated to handle the particle re-positioning in the different resolution levels. The proposed algorithms can be straightforwardly implemented in an SPH model without requiring cumbersome code modifications. The δ + -SPH is validated on seven different benchmarks giving a wide panorama on the improvements of this new SPH model.

During the process of wave slamming on a structure with sharp corners, the wave receding after wave impingement can induce strong negative pressure (relative to the atmospheric pressure) at the bottom of the structure, which is called the suction effect. From the practical point of view, the suction force induced by the negative pressure, coinciding with the gravity force, pulls the structure down and hence increases the risk of structural damage. In this work, the smoothed particle hydrodynamics (SPH) method, more specifically the δ+SPH model, is adopted to simulate the freak wave slamming on a fixed platform with the consideration of the suction effect, i.e., negative pressure, which is a challenging issue because it can cause the so-called tensile instability in SPH simulations. The key to overcome the numerical issue is to use a numerical technique named tensile instability control (TIC). Comparative studies using SPH models with and without TIC will show the importance of this technique in capturing the negative pressure. It is also found that using a two-phase simulation that takes the air phase into account is essential for an SPH model to accurately predict the impact pressure during the initial slamming stage. The freak wave impacts with different water depths are studied. All the multiphase SPH results are validated by our experimental data. The wave kinematics/dynamics and wave impact features in the wave-structure interacting process are discussed, and the mechanism of the suction effect characterized by the negative pressure is carefully analyzed.

The present work is dedicated to an accurate modeling of violent Fluid-Structure-Interaction (FSI) problems using a coupled Lagrangian particle method combining a multi-phase δ-SPH scheme and a Total-Lagrangian-Particle (TLP) method. Advanced numerical techniques, e.g. Adaptive-Particle-Refinement (APR), have been included in the particle method for improving the local accuracy and the overall numerical efficiency. On one hand, this paper aims to demonstrate the capability of the proposed numerical method in modeling FSI flows with large density-ratios, strong fluid impacts, complex interfacial evolutions and considerable wall-boundary movements and deformations; On the other hand, the numerical results presented in this paper show the importance of considering the existence of air-phase in some complex FSI problems. The entrapped air-bubble, after the free-surface rolling and closing, plays an important role in the overall flow evolution and hence the hydrodynamic load on the structure. Although a density ratio as large as 1000 has been adopted, clear and sharp multi-phase interfaces, which undergo violent breakups and reconnections, are present in the numerical results, and more importantly, stable and smooth pressure fields are obtained. This contributes to an accurate prediction of the structural response, as validated by both the experimental data and other numerical results.

Non-reflecting boundary conditions (NRBCs) play an important role in computational fluid dynamics (CFD). A novel NRBC based on the method of characteristics using timeline interpolations is proposed for fluid dynamics solved by smoothed particle hydrodynamics (SPH). It is performed by four layers of particles whose pressures and velocities are obtained through the Lagrange interpolation in the time domain which is derived from the propagation of characteristic waves between particles. The proposed NRBC can allow outward travelling pressure and velocity messages to pass through the boundary without obvious reflection. That is, with the implementation of the NRBC, the solution in a finite computational domain of interest is close to that in an infinite domain. Several numerical tests show that this NRBC is robust and applicable for a broad variety of hydrodynamics ranging from low to high speed.

Ditching often takes place for a ground-effect wing (WIG) ship. During the ditching, the extreme load developed by water impacts may cause damages to structures, posing a great threat to the safety of crew and passengers. In the paper, a weakly compressible smoothed particle hydrodynamics (SPH) model combined with enhanced numerical techniques has been adopted to tackle the ditching problems. In order to handle the motion of a rigid body in the three-dimensional ditching problems, the six degrees-of-freedom (6-DOF) equations of motion are incorporated into the SPH scheme. The accuracy of the SPH model is validated through two benchmarks, respectively, the two-dimensional wedge water entry and the three-dimensional stone-skipping. The former is aimed to validate the prediction of pressures during the free surface impact while the latter is a good case for testing the coupling motions of the rigid body. Furthermore, the ditching of the real scale WIG ship under different conditions is simulated with the established SPH model, through which some useful conclusions are drawn.

In the present work, the single-phase and weakly-compressible δ-SPH model is further extended to simulate multiphase and strongly-compressible flows. This is motivated by the fact that traditional SPH models can meet some difficulties when modeling strongly-compressible flows with large volume variations (e.g. expansion and collapse of cavitation bubbles). Due to the strong compressibility of the fluid, the energy equation should be considered in the governing equations. In that case, the pressure is solved based on both density and internal energy. To stabilize the pressure field, density and energy diffusive terms should be applied. Large variations of particle volumes in the compressible phase would result in large variations of particle spacing. Therefore, particle smoothing lengths are adjusted in time to maintain appropriate neighboring particles. To ensure good properties of accuracy and conservation when particles with different smoothing lengths interact, corrected SPH operators are utilized to discretize the governing equations. Moreover, in order to limit the particle volume variations and maintain a homogeneous volume distribution in the entire flow field, especially near the interface between different phases of different compressibility, a new volume adaptive scheme is proposed to control particle volumes. The volumes which are over-expanded or over-compressed will be split or merged with others, maintaining a small particle volume variation in the flow. Finally, the proposed SPH model is validated with several challenging benchmarks including expansion and collapse of underwater-explosion bubbles or cavitation bubbles. All the SPH results are compared with other numerical solutions with good agreements.

The recently developed FSI-SPH model (Sun et al., 2019c), by combining the multi-resolution δ + -SPH scheme and a Total Lagrangian SPH method, is further extended for more complex three-dimensional (3D) Fluid Structure Interaction (FSI) problems. The FSI-SPH model is strengthened with advanced numerical techniques, in which a combination of the Particle Shifting Technique (PST) and the Tensile Instability Control (TIC) is adopted to prevent flow voids induced by the tensile instability. The Adaptive Particle Refinement (APR) is used to refine particles in the boundary layer region and coarsen particles in the far-field to increase local accuracy but reduce overall computational cost. Moreover, the δ + -SPH and Total Lagrangian SPH solvers are coupled through a Modified Sequential Staggered (MSS) algorithm which, on one hand, ensures the numerical accuracy and stability and, on the other hand, improves the efficiency when magnitudes of time steps between the two solvers differ from each other significantly. In the numerical results, challenging 2D and 3D FSI cases are simulated to test the accuracy of the proposed FSI-SPH model. A new FSI benchmark with free-surface is proposed to highlight the advantage of this FSI-SPH model in simulating free-surface viscous flows. In addition, 3D effects in the FSI dam-breaking and sloshing cases are investigated.

The behaviour of a weakly-compressible SPH scheme obtained by rewriting the Navier-Stokes equations in an arbitrary Lagrangian-Eulerian (ALE) format is studied. Differently from previous works on ALE, which generally adopt conservative variables (i.e. mass and momentum) and rely on the use of Riemann solvers inside the spatial operators, the proposed model is expressed in terms of primitive variables (i.e. density and velocity) and is written by using the standard differential formulations of the weakly-compressible SPH schemes. Similarly to ALE-SPH models, the arbitrary velocity field is obtained by modifying the pure Lagrangian velocity of the material point through a velocity δ u → given by a Particle Shifting Technique (PST). We show that the above-mentioned ALE-SPH equations are, however, unstable when they are integrated in time. The instability appears in the form of large volume variations in those fluid regions characterised by high velocity strain rates. Nonetheless, the scheme can be stabilised if appropriate diffusion terms are included in both the equations of density and mass. This latter scheme, hereinafter called δ -ALE-SPH scheme, is validated against reference benchmark test-cases: the viscous flow around an inclined elliptical cylinder, the lid-driven cavity and a dam-break flow impacting a vertical wall.

The present work is dedicated to extending the strongly-compressible multiphase SPH Volume Adaptive Scheme (see [22] ) from Cartesian to cylindrical polar coordinates for addressing axisymmetric problems. By omitting the gradient in the circumferential direction, an Axisymmetric-SPH model is developed. Three-dimensional axisymmetric problems including rising bubbles, expanding or collapsing bubbles are conveniently and efficiently simulated using the proposed Axisymmetric-SPH model. Contrary to the purely three-dimensional SPH model established in Cartesian coordinates, with the axisymmetric model, sufficient particle resolutions can be easily adopted to reach converged simulations of complex problems. Axisymmetric-SPH results are validated either using experimental data or other numerical results. In the Axisymmetric-SPH model, a convenient and effective way of avoiding singularity at the axis is presented. In addition, the Volume Adaptive Scheme (VAS), originally developed for compressible flow simulations with large volume variations in Cartesian coordinates, is shown to be a crucial tool to adjust particle volumes in the Axisymmetric-SPH model for all flow cases, including both weakly-compressible and strongly-compressible flows.

The present work is dedicated to the detection of Lagrangian Coherent Structures (LCSs) in viscous flows through the Finite-Time Lyapunov Exponents (FTLEs) which have been addressed by several works in the recent literature. Here, a novel numerical technique is presented in the context of the Smoothed Particle Hydrodynamics (SPH) models. Thanks to the Lagrangian character of SPH, the trajectory of each fluid particle is explicitly tracked over the whole simulation. This allows for a direct evaluation of the FTLE field supplying a new way for the data analysis of complex flows. The evaluation of FTLE can be either implemented as a post-processing or nested into the SPH scheme conveniently. In the numerical results, three test-cases are presented giving a proof of concept for different conditions. The last test-case regards a naval engineering problem for which the present algorithm is successfully used to capture the submerged vortical tunnels caused by the splashing bow wave.

In the marine and ocean engineering area, the water-entry process is a typical problem of fluid-solid interaction, which involves complex phenomenon such as the large deformation of free surface and considerable structure movement. In this process, the predicting impact load and summarizing the evolution law of the free surface deformation have important reference significance for the hull structure design. To address this issue, numerical simulations are carried out using a robust Smoothed Particle Hydrodynamics (SPH) model. The accuracy of the present SPH model is firstly validated by simulating the water entry of bow-flare section in two and three dimensions, respectively. Then, we investigate the variation characteristics of impact load and the evolution of free surface during the entry of the bow-flare ship section with different roll angles ( θ = 0 ∘ ∼ 20 . 3 ∘ ). Attention is focused on the flow separating phenomenon and the spray jet on the free surface. Finally, the water entry of a three dimensional ship hull is simulated. The velocity and pressure of flow field are analyzed and some conclusions are drawn.

3-D SPH simulations are often time-consuming due to the massive particle numbers. For the problem which has axisymmetric characteristics, the solving of the entire three-dimensional domain can be simplified which saves computational cost dramatically. In this paper, a novel derivation for the SPH formulation in cylindrical coordinate is presented, which is straightforward and physically meaningful. A multiphase numerical model is developed based on the derived formulation including the discretization formulas of surface tension force, viscous force, interface sharpness force and the treatment of high density ratio near the multiphase interface, as well as an improved anti-penetration treatment close to the axis. The effectiveness and robustness of the proposed multiphase SPH model are demonstrated via the classical surface-tension test and bubble rising problems at different conditions. The results are compared with analytical solutions, the experimental data and other numerical results. The promising results of the novel axisymmetric SPH model demonstrate a great potential for an efficient SPH modeling of complex axisymmetric multiphase flows. Dramatic efficiency boost is achieved by comparing the axisymmetric simulation with 3-D simulation in terms of CPU time.

A multiphase SPH model based on Roe’s approximate Riemann solver is proposed to simulate complex interfacial flows in hydraulics. In this multiphase model, the solution to a one-dimensional Riemann problem is introduced into the SPH governing equations to determine the interaction between particles. The Riemann problem is solved by Roe’s approximate Riemann solver which may introduce excessive numerical dissipations. To reduce these dissipations, a dissipation limiter is applied. An equivalent relation between the dissipation term in the dissipation limiter and the Reynolds number is derived to model viscous flows of different Reynolds numbers. For flows of high density ratios (up to 1000), stable and smooth interfacial pressure can be obtained. The realistic compressibility can be considered for the light fluid and a larger time step can be allowed, leading to a decrease of the computational cost. To further make the simulation more efficient, an optimized adaptive linked-list search algorithm is introduced. Using this optimized algorithm, the particle interaction list can be updated every dozen of time steps instead of at each time step, which contributes to a significant reduction of the total computational cost. Seven numerical tests are presented to validate this multiphase model.

It is well known that the use of SPH models in simulating flow at high Reynolds numbers is limited because of the tensile instability inception in the fluid region characterized by high vorticity and negative pressure. In order to overcome this issue, the δ + -SPH scheme is modified by implementing a Tensile Instability Control (TIC). The latter consists of switching the momentum equation to a non-conservative formulation in the unstable flow regions. The loss of conservation properties is shown to induce small errors, provided that the particle distribution is regular. The latter condition can be ensured thanks to the implementation of a Particle Shifting Technique (PST). The novel variant of the δ + -SPH is proved to be effective in preventing the onset of tensile instability. Several challenging benchmark tests involving flows past bodies at large Reynolds numbers have been used. Within this a simulation characterized by a deforming foil that resembles a fish-like swimming body is used as a practical application of the δ + -SPH model in biological fluid mechanics.

The present work is dedicated to the application of the recently developed (δ+-SPH) scheme to the self-propulsive fishlike swimming hydrodynamics. In the numerical method, a particle shifting technique (PST) is implemented in the framework of δ-SPH, combining with an adaptive particle refinement (APR) which is a numerical technique adopted to refine the particle resolution in the local region and de-refine particles outside that region. This comes into being the so-called δ+-SPH scheme which contributes to higher numerical accuracy and efficiency. In the fishlike swimming modeling, a NACA0012 profile is controlled to perform a wavy motion mimicking the fish swimming in water. Thanks to the mesh-free characteristic of SPH method, the NACA0012 profile can undergo a wavy motion with large amplitude and move forward freely, avoiding the problem of mesh distortion. A parallel staggered algorithm is adopted to perform the fluid-structure interaction between the foil and the surrounding fluid. Two different approaches are adopted for the fishlike swimming problem. In Approach 1, the foil is fixed and flaps in a free stream and in Approach 2, the wavy foil can move forward under the self-driving force. The numerical results clearly demonstrate the capability of the δ+-SPH scheme in modeling such kind of self-propulsive fishlike swimming problems. Keywords: Smoothed particle hydrodynamics, δ+-SPH, Fishlike swimming, Wavy foil, Swimming propulsion

A robust weakly compressible SPH method is applied to simulate violent interactions between free surface and rigid body. Artificial density and viscosity diffusion are applied to stabilize the pressure field. The calculation of forces and torques on rigid body is improved for higher accuracy. Improved dummy particle technique for stationary and moving boundary is analyzed and applied in both free-slip and no-slip condition. For the velocity divergence approximation near the dummy particle boundary, it is proved that substituting the velocity of the rigid body directly into the divergence operator is acceptable and reasonable. For the viscous stress calculation, the dummy particle velocity extension manners in both free-slip and no-slip boundary condition are given in higher accuracy. The present solid boundary technique is convenient for both two-dimensional (2-D) and three-dimensional (3-D) models. Stability and accuracy of the present SPH scheme are tested by four 2-D cases and two 3-D cases, and the results agree well with both experimental data and other numerical results. The present SPH scheme is potential for some ocean engineering applications with violent fluid–solid interactions.

In ocean engineering, the applications are usually related to a free surface which brings so many interesting physical phenomena (e.g. water waves, impacts, splashing jets, etc.). To model these complex free surface flows is a tough and challenging task for most computational fluid dynamics (CFD) solvers which work in the Eulerian framework. As a Lagrangian and meshless method, smoothed particle hydrodynamics (SPH) offers a convenient tracking for different complex boundaries and a straightforward satisfaction for different boundary conditions. Therefore SPH is robust in modeling complex hydrodynamic problems characterized by free surface boundaries, multiphase interfaces or material discontinuities. Along with the rapid development of the SPH theory, related numerical techniques and high-performance computing technologies, SPH has not only attracted much attention in the academic community, but also gradually gained wide applications in industrial circles. This paper is dedicated to a review of the recent developments of SPH method and its typical applications in fluid-structure interactions in ocean engineering. Different numerical techniques for improving numerical accuracy, satisfying different boundary conditions, improving computational efficiency, suppressing pressure fluctuations and preventing the tensile instability, etc., are introduced. In the numerical results, various typical fluid-structure interaction problems or multiphase problems in ocean engineering are described, modeled and validated. The prospective developments of SPH in ocean engineering are also discussed.

As a Lagrangian meshless method, smoothed particle hydrodynamics (SPH) method is robust in modelling multi-fluid flows with interface fragmentations. However, the application for the simulation of a rising bubble bursting at a fluid surface is rarely documented. In this paper, the multiphase SPH model is extended and applied to simulate this challenging phenomenon. Different numerical techniques developed in different SPH models are combined in the present SPH model. The adoption of a background pressure determined based on the surface tension can help to avoid tensile instability and interface penetrations. An accurate surface tension model is employed. This model is suitable for bubble rising problems of small scales and high density ratios. An interface sharpness force is adopted to achieve a smoother bubble surface. A suitable formula of viscous force, which is proven to be able to accurately capture the bubble splitting and small bubble detachment, is employed. Moreover, a modified prediction-correction time-stepping scheme for a better numerical stability and allows a relatively larger CFL factor is adopted. It is also worthwhile to mention that the particle shifting technique, which helps to make the particle distribute in an arrangement of lower disorder, can significantly improve the numerical accuracy. Regarding the treatment of the fluid surface, particles of lighter phase are arranged above the free surface of the denser phase to avoid the kernel truncation in the density approximation. Furthermore, this technique also allows an accurate calculation of the surface tension on the fluid surface. A number of cases of bubbly flows are presented, which confirms the capability of the present multiphase SPH model in modelling complex bubble-surface interactions with the density ratio and viscosity ratio up to 1000 and 100 respectively.

The present work is dedicated to the modeling of viscous flow past a NACA0012 foil fixed in a current below a free surface. To this end, the [Formula: see text]-smoothed-particle hydrodynamics (SPH) model has been adopted. This SPH model prevents the inception of the numerical tensile instability in the flow region characterized by negative pressure since a tensile instability control (TIC) has been included. In the TIC, a pressure differencing formulation (PDF) has been adopted for the momentum equation in the flow region characterized by negative pressure. In order to completely remove the numerical noise in the vorticity field, in this work, the PDF is also applied for the region with positive pressure, but except for the free-surface region in order to ensure the free surface stability when wave breaking occurs. The mechanism of PDF being able to eliminate the numerical noise in the vorticity field is also briefly analyzed. In order to reduce the nonconservation of total momentum induced by the PDF, a particle-shifting technique (PST) is implemented in each time step for regularizing the particle position. In the numerical results, [Formula: see text]-SPH results are validated by the experimental data and other verified numerical results. Improvements of the results of [Formula: see text]-SPH with PDF with respect to the ones without using PDF are demonstrated. Parametrical studies based on the [Formula: see text]-SPH model regarding the breaking and non-breaking waves generated by the flow past a submerged foil are also carried out.