Shared-Memory parallelization of consistent particle method for violent wave impact problems

A shared-memory parallelization is implemented to the recently developed Consistent Particle. Method (CPM) for violent wave impact problems. The advantages of this relatively new particle method lie in four key aspects: (1) accurate computation of Laplacian and gradient operators based on Taylor series expansion, alleviating spurious pressure fluctuation and being able to model two-phase flows characterized by large density difference, (2) a thermodynamics-based compressible solver for modelling compressible air that eliminates the need of determining artificial sound speed, (3) seamless coupling of the compressible air solver and incompressible water solver, and (4) parallelization of the numerical model based on Open Multi-Processing (OpenMP) and a parallel direct sparse solver (Pardiso) to significantly improve computational efficiency. Strong and weak scaling analyses of the parallelized CPM are conducted, showing an efficiency speedup of 100 times or more depending on the size of simulated problem. To demonstrate the accuracy of the developed numerical model, three numerical examples are studied including the benchmark study of wave impact on seawall, and our experimental studies of violent water sloshing under rotational excitations and sloshing impact with entrapped air pocket. CPM is shown to accurately capture highly deformed breaking waves and violent wave impact pressure including pressure oscillation induced by air cushion effect.     

Hydrodynamic characteristics of a cylindrical bottom-pivoted wave energy absorber

A parametric study was carried out to investigate the hydrodynamics of a cylindrical wave energy absorber. Established methods of hydrodynamic analysis were applied to the case of a damped vertically oriented cylinder pivoted near the sea floor in intermediate depth water. The simple geometry provides a canonical reference for more complex structure shapes and configurations that may be considered for either wave energy conversion or wave energy absorption. The study makes use of the relative velocity Morison equation, with force coefficients derived from radiation and diffraction theory. Viscous effects were accounted for by including a drag term with an empirically derived coefficient, C_D. A non-linear first-order formulation was used to calculate the cylinder motion response in regular waves. It was found that the non-linear drag term, which is often neglected in studies on wave energy conversion, has a large effect on performance. Results from the study suggest a set of design criteria based on Keulegan–Carpenter (KC) number, ratio of cylinder radius to water depth (a/h), and ratio of water depth to wavelength (h/L). Respectively, these parameters account for viscous, wave radiation, and water depth effects, and optimal ranges are provided.     

Experimental and numerical studies on the development of a new wave absorber

This paper proposes a new wave absorber made of flexible net structures. To test the efficiency of the proposed water absorber, experiments were done on wave absorbers of various lengths of and the thicknesses of the wave absorber. To perform a numerical modeling of the proposed wave absorber, damping terms were introduced in linearized free-surface boundary conditions. The length and the thickness of the wave absorber were modeled by the length and the coefficient of the damping zones. The boundary element method was adopted to solve the system. Series of experiments were performed to obtain the data for the coefficients of the damping term needed in numerical calculations. The predicted wave heights agreed very closely with those of experiments when the lengths of the incoming waves were within the order of the length of the wave absorber.     

Probability models for offshore structural response due to Morison wave loading Part I: Drag-only response

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of their response to wave loading is a minimum requirement for efficient probabilistic analysis of these structures. Due to nonlinearity of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian. Analysis of simulated data has, however, shown that neither of the two probability models proposed in the literature can accurately predict the tails of the response distribution. New probability models are therefore required to overcome this deficiency. This paper is composed of two parts: Part I is devoted to the development and validation of a new probability model for drag-only responses (i.e. responses due to the drag component of Morison wave loading), while Part II is devoted to the development and validation of new probability models for both inertia-only and total responses.     

Enhanced predictions of wave impact pressure by improved incompressible SPH methods

A new criterion is proposed for a more efficient assessment of free-surface particles in a particle-based simulation. Enhanced wave impact simulations are carried out by improved Incompressible SPH (ISPH) methods. The first improvement is the same as that in the Corrected ISPH (CISPH; [Khayyer A, Gotoh, H, Shao SD. Corrected incompressible SPH method for accurate water-surface tracking in breaking waves, Coast Eng 2008; 55 (3): 236–250]) method and is proposed for the improvement of momentum conservation. The second improvement is achieved by deriving and employing a higher order source term based on a more accurate differentiation to obtain a less fluctuating and more accurate pressure field. The enhanced performance of improved ISPH methods is demonstrated through the simulation of several fluid impact simulations in comparison with the experimental data and simulation results by other numerical methods.     

Dynamic analysis of a vertical plate exposed to breaking wave impact

From the experimental studies in recent years, it has become known that when a wave breaks directly on a vertical faced coastal structure, high magnitude impact pressures are produced. The theoretical and experimental studies show that the dynamic response of such structures under wave impact loading is closely dependent on the magnitude and duration of the load history. The dynamic analysis and design of a coastal structure can be succeeded provided the design load history for the wave impact is available. Since these types of data are very scarce, it is much more convenient to follow a method which is based on static analysis for the dynamic design procedure. Therefore, to facilitate the dynamic design of a vertical plate that is exposed to breaking wave impact, a multiplication factor called “dynamic magnification factor” is herein presented which is defined as the ratio of the maximum value of the dynamic response to that found by static analysis. The computational results of the present study show that the dynamic magnification factor is a useful ratio to transfer the results of static analysis to the dynamic design of a coastal plate for the maximum impact pressure conditions of p_max/γH₀≤18.     

Modified Moving Particle Semi-implicit methods for the prediction of 2D wave impact pressure

As a gridless particle method, the MPS (Moving Particle Semi-implicit) method has proven useful in a wide variety of engineering applications including free-surface hydrodynamic flows. Despite its wide range of applicability, the MPS method suffers from some shortcomings such as non-conservation of momentum and spurious pressure fluctuation. By introducing new formulations for the pressure gradient and a new formulation of the source term of the Poisson Pressure Equation (PPE), and by allowing a slight compressibility, we have proposed modified MPS methods for the prediction of wave impact pressure on a coastal structure. The improved performance of the modified methods is shown through the simulation of numerous wave impact problems (including the impacts by a dam break flow, a flip-through and two cases of slightly-breaking waves) in comparison with the experimental data.     

Impulse modelling of wave impact pressures on vertical wall

Breaking waves on coastal structures cause high magnitude impact pressures which may be important for the structural stability. In estimating the impact pressure distribution on the wall, there have been a lot of theoretical and experimental work. The present study is concerned with a theoretical approach which is based on the pressure impulse, to find the impact pressures on vertical wall. The numerical solution of the governing equation is carried out using the boundary element method. The theoretical impact pressures are determined using the experimental values of impact pressure rising time. The computational results of the impact pressures from the pressure impulse model are found to agree well with the experimental data of an earlier study.     

Probability models for offshore structural response due to Morison wave loading: Part II: Inertia-only and total responses

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of their response to wave loading is a minimum requirement for efficient probabilistic analysis of these structures. Due to nonlinearity of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian. Part I of this paper was devoted to the development and validation of a new probability model for drag-only responses (i.e. responses due to the drag component of Morison wave loading). This part is devoted to the development and validation of new probability models for both inertia-only and total responses.     

Numerical simulation of sloshing waves in a 3D tank based on a finite element method

The sloshing waves in a three dimensional (3D) tank are analysed using a finite element method based on the fully non-linear wave potential theory. When the tank is undergoing two dimensional (2D) motion, the calculated results are found to be in very good agreement with other published data. Extensive calculation has been made for the tank in 3D motion. As in 2D motion, in addition to normal standing waves, travelling waves and bores are also observed. It is found that high pressures occur in various circumstances, which could have important implications for many engineering designs.     

Modelling analysis of the sensitivity of shoreline change to a wave farm

Change of shoreline wave climate caused by the installation of a wave farm is assessed using the SWAN wave model. The 30 MW-rated wave farm is called the ‘Wave Hub’ and will be located 20 km off the north coast of Cornwall, UK. Changes in significant wave height and mean wave period due to the presence of the Wave Hub are presented. The results suggest that the shoreline wave climate will be affected, although the magnitude of effects decreases linearly as wave energy transmitted increases. At probable wave energy transmission levels, the predicted change in shoreline wave climate is small.     

Nonlinear modeling of liquid sloshing in a moving rectangular tank

A nonlinear liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be homogeneous, isotropic, viscous, Newtonian and exhibit only limited compressibility. The tank is forced to move harmonically along a vertical curve with rolling motion to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface. The model solves the complete Navier–Stokes equations in primitive variables by use of the finite difference approximations. At each time step, a donor–acceptor method is used to transport the volume of fluid function and hence the locations of the free surface. In order to assess the accuracy of the method used, computations are verified through convergence tests and compared with the theoretical solutions and experimental results.     

聚焦波作用下立柱高阶波浪力特性研究

以方形立柱作为研究对象,对其在聚焦波作用下的波浪力特性进行研究。研究主要基于计算流体力学数值方法,对聚焦波作用下方形立柱在固定、单自由度纵荡、单自由度垂荡三种运动状态下所受波浪力进行研究。利用phase-inversion逆相位分解方法对其高阶力特性进行分析。首先对聚焦波生成方法、数值计算方法与参数设置进行简要介绍,其次展示了三种运动状态下立柱在聚焦波作用下所受波浪力,并对其进行分析,最后利用phase-inversion逆相位分解方法获得高阶波浪力成分并对其载荷特性进行分析讨论。研究发现逆相位分解方法可以有效分离波浪力高阶成分,不同运动状态下立柱所受波浪力会有显著不同。     

Application of an improved semi-Lagrangian procedure to fully-nonlinear simulation of sloshing in non-wall-sided tanks

The semi-Lagrangian procedure is widely used for updating the fully-nonlinear free surface in the time domain. However, this procedure is only available to cases when the body surface is vertical near the waterline. Present study introduces an improved semi-Lagrangian procedure which removes this ‘vertical-wall’ limitation. Coupling with the boundary element method, the improved semi-Lagrangian procedure is applied to the simulation of fully-nonlinear sloshing waves in non-wall-sided tanks. From the result comparison with the open source CFD software OpenFOAM, it is confirmed that this numerical scheme could guarantee a sufficient accuracy. Further series studies on 2D and 3D fully-nonlinear sloshing waves in wedged tanks are performed. Featured phenomena are observed which are distinct from those in wall-sided tanks.     

Analysis of the extreme wave elevation due to second-order diffraction around a vertical cylinder

Statistical analysis of nonlinear random waves is important in coastal and ocean engineering. One approach for modeling nonlinear waves is second-order random wave theory, which involves sum- and difference-frequency interactions between wave components. The probability distribution of the non-Gaussian surface elevation can be solved using a technique developed by Kac and Siegert [21]. The wave field can be significantly modified by wave diffraction due to a structure, and the nonlinear diffracted wave elevation can be of interest in certain applications, such as the airgap prediction for an offshore structure. This paper investigates the wave statistics due to second-order diffraction, motivated by the scarcity of prior research. The crossing rate approach is used to evaluate the extreme wave elevation over a specified duration. The application is a bottom-supported cylindrical structure, for which semi-analytical solutions for the second-order transfer functions are available. A new efficient statistical method is developed to allow the distribution of the diffracted wave elevation to be obtained exactly, accounting for the statistical dependency between the linear, sum-frequency and difference-frequency components. Moreover, refinements are proposed to improve the efficiency for computing the free surface integral. The case study yields insights into the problem. In particular, the second-order nonlinearity is found to significantly amplify the extreme wave elevation, especially in the upstream region; conversely, the extreme elevation at an oblique location downstream is attenuated due to sheltering effects. The statistical dependency between the linear and sum-frequency components is also shown to be important for the extreme wave statistics.     

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

The numerical and experimental investigations on the performance of an offshore-submerged breakwater in reducing the wave forces and wave run-up on vertical wall are presented. A two-dimensional finite-element model is employed to study the hydrodynamic performance of the submerged breakwater under the action of regular and random waves. The numerical prediction has been supported with experimental measurements. The wave forces and wave run-up on the vertical wall were measured for different breakwater configurations. The applicability of linear theoretical model in the prediction of wave forces on the wall by a submerged breakwater has been discussed.     

Wavelet transform based coherence analysis of freak wave and its impact

The present paper presents the results of a wavelet transform-based coherence analysis of freak wave and its impact. Wavelet transform has been used as a tool in analyzing signals in the time domain as well as in the frequency domain. The analysis was applied to laboratory-generated freak waves. The wavelet transform of the time history of the freak wave and its impact force revealed that a wide range of frequency components were contained in them. The coherence analysis was conducted on the wave and its impact force time histories. The coherence analysis revealed that some high-frequency components were highly correlated with the impact forces. The present study demonstrates that the wavelet transform can be an alternative tool in the analysis of strongly nonlinear freak wave and its impact.     

Numerical study of nonlinear freak wave impact underneath a fixed horizontal deck in 2-D space

Freak waves are extreme and unexpected surface waves with huge wave heights that may lead to severe damage to ships and offshore structures. However, few researches have been conducted to investigate the impact underneath fixed horizontal decks caused by freak waves. To study these phenomena, a 2-D numerical wave tank is built in which nonlinear freak waves based on the Peregrine breather solution are generated. As a validation, a regular-wave-induced underneath impact is simulated and compared to the existing experimental measurements. Then the nonlinear freak-wave-induced impact is investigate with different values of deck clearance above the mean free surface. In addition, a comparative simulation of a “large” regular wave based on the 2nd-order Stokes wave theory with the same crest height and wave length of the nonlinear freak wave is carried out to reveal the unique features of the nonlinear freak-wave-induced impact. By applying a fluid–structure interaction (FSI) algorithm in which the bottom deck and front side wall are simplified as Euler beams in 2-D and discretized by the finite element method (FEM), the hydroelastic effects are considered during the impact event. The vertical force acting underneath the bottom deck, the transversal force acting on the front side wall, the structural displacements of the elastic deck and wall are analyzed and discussed respectively, from which meaningful conclusions are drawn.     

An efficient hybrid integral-equation method for point-absorber wave energy converters with a vertical axis of symmetry

To assist in the prototyping and controller design of point-absorber wave energy converters (WECs), an easy-to-implement hybrid integral-equation method is presented for computing the frequency-domain hydrodynamic properties of bodies with a vertical axis of symmetry in waves. The current hybrid method decomposes the flow domain into two parts: an inner domain containing the body and an outer domain extending to infinity. The solution in the inner domain is computed using the boundary-element method, and the outer-domain solution is expressed using eigenfunctions. Proper matching at the domain boundary is achieved by enforcing continuity of velocity potential and its normal derivative. Body symmetry allows efficient computation using ring sources in the inner domain. The current method is successfully applied to three different body geometries including a vertical truncated floating cylinder, the McIver toroid, and the coaxial-cylinder WEC being developed in the authors’ laboratory. In particular, the current results indicate that, by replacing the flat bottom of the coaxial-cylinder WEC with the Berkeley-Wedge (BW) shape, viscous effect can be significantly reduced with only minor negative impact on wave-exciting force, thus increasing WEC efficiency. Finally, by comparing to experimental measurements, the current method is demonstrated to accurately predict the heave added mass and wave-exciting force on the coaxial-cylinder WEC with BW geometry. If a viscous damping correction factor is used, the heave motion amplitude can also be accurately computed.     

Experimental study on mechanism of sea-dike failure due to wave overtopping

This work, which was largely a fruit of China's national marine hazard mitigation service, explicitly reveals the major mechanism of sea-dike failure during wave overtopping. A large group of wave-flume experiments were conducted for sea dikes with varying geometric characteristics and pavement types. The erosion and slide of the landward slope due to the combined effect of normal hit and great shear from overtopping flows was identified the major trigger of the destabilization of sea dikes. Once the intermittent hydrodynamic load and swash caused any deformation (bump or dent) of the pavement layer, pavement fractions (slabs or rubble) on the slope started to be initiated and removed by the water. The erosion of the landward slope was then gradually aggravated followed by entire failure within a couple of minutes. Hence, the competent velocity would be helpful evaluate the failure risk if as well accounted in standards or criteria. However, the dike top was measured experiencing the largest hydrodynamic pressure with a certain cap while the force on the wall increased rapidly as the overtopping intensity approached the dike-failure threshold. The faster increase of the force on the wall than on the landward slope yielded the sequencing of loads reaching hypothetic limits before failure as: dike top – top-mounted wall – landward slope. Therefore, beside the slide failure, the fatigue damage due to the instantaneous hydrodynamic impact might be another mechanism of the dike failure, which did not appear in the experiment but should be kept in mind. Instead of the widely adopted tolerable overtopping rate, a 0.117–0.424 m³/(m s) range of overtopping discharge and a 10 m/s overtopping velocity for the failure risk of typical sea dikes along China's coastlines were suggested, which enables the possible failure risk prediction through empirical calculations. The failure overtopping rate was identified strongly dependent on the pavement material, the landward slope and the dike-mounted wall but showed little variation with the width of the dike top. The flat concrete pavement and gentle landward slopes are suggested for the dike design and construction. For given configurations and hydrodynamic conditions in the experiment, the dike without the wall experienced less overtopping volume than those with the 1-m top-mounted wall. Meanwhile, the remove of the wall increased the failure overtopping rate, which means a certain increase of the failure criterion. Thus, care must be taken to conclude that the dike-mounted wall seems not an entirely appropriate reinforcement for the stability and safety of coastal protections. This should be further checked and discussed by researchers and engineers in the future.