A two-dimensional numerical wave flume based on SA-MPLS method

A spatially adaptive (SA) two-dimensional (2-D) numerical wave flume is presented based on the quadtree mesh system,in which a new multiple particle level set (MPLS) method is proposed to solve the problem of interface tracking,in which common intersection may be traversed by multiple interfaces.By using the adaptive mesh technique and the MPLS method,mesh resolution is updated automatically with time according to flow characteristics in the modeling process with higher resolution around the free surface and the solid boundary and lower resolution in less important area.The model has good performance in saving computer memory and CPU time and is validated by computational examples of small amplitude wave,second-order Stokes wave and cnoidal wave.Computational results also indicate that standing wave and wave overtopping are also reasonably simulated by the model.

Numerical simulation for the two-dimensional nonlinear shallow water waves

This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.

Numerical Model of Cnoidal Wave Flume

The volume of fluid (VOF) method is used to set up a wave flume with an absorbing wave maker of cnoidal waves. Based on the transfer function between wave surface and paddle velocity obtained by the shallow water wave theory, the velocity boundary condition of an absorbing wave maker is introduced to absorb reflected waves that reach the numerical wave maker. For Hid ranging from 0.1 to 0.59 and T root g/d from 7.9 to 18.3, the parametric studies have been carried out and compared with experiments.

Establishment of Numerical Wave Flume Based on the Second-Order Wave-Maker Theory

With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume.

Extreme Wave Simulation with Iterative Adaptive Approach in Numerical Wave Flume

Extreme wave is highly nonlinear and may occur due to diverse reasons unexpectedly.The simulated results of extreme wave based on wave focusing,which were generated using high order spectrum method,are presented.The influences of the steepness,frequency bandwidth as well as frequency spectrum on focusing position shift were examined,showing that they can affect the wave focusing significantly.Hence,controlled accurate generation of extreme wave at a predefined position in wave flume is a difficult but important task.In this paper,an iterative adaptive approach is applied using linear dispersion theory to optimize the control signal of the wavemaker.The performance of the proposed approach is numerically investigated for a wide variety of scenarios.The results demonstrate that this approach can reproduce accurate wave focusing effectively.

Numerical study of resonance induced by wave action on multiple rectangular boxes with narrow gaps

By introducing a source term into the Laplace equation, a two-dimensional fully nonlinear time-domain numerical wave flume （NWF） is developed to investigate the resonance induced by the interaction between waves and multiple objects with narrow gaps. In the numerical model, the fully nonlinear kinematic and dynamic boundary conditions are satisfied on the instantaneous free surface and the constant artificial damping is employed in the gaps to approximate the viscous dissipation due to vortex motion and flow separation. The computational domain is discretized using a higher-order boundary element method （HOBEM）. The proposed model is firstly validated against the published experimental data and numerical results of the wave height in the narrow gap between two boxes, the wave heights in the two gaps of three boxes, and wave loads on the boxes. Then, the extensive numerical experiments are performed to study the influences of the number of the boxes and the gap spacing on the resonant frequency, reflected and transmitted wave heights and wave loads on the boxes.

Numerical Simulation of Irregular Wave Overtopping Against A Smooth Sea Dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model, a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes. Simulations of fully nonlinear standing wave and regular wave＇s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules. To model stationary ergodic stochastic processes, several cases with different random seeds are computed for each specified irregular wave spectrum. It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas, other numerical results and experimental data.

Numerical investigation of solitary wave action on tworectangular boxes with a narrow gap

Based on the time-domain higher-order boundary element method(HOBEM), a two-dimensional numerical wave flume is developed to investigate solitary wave interaction with two rectangular boxes with a narrow gap.In the numerical model, the fully nonlinear boundary conditions are satisfied on the free surface, the mixed Eulerian-Lagrangian method is adopted to track the transient water surface and the fourth-order Runga-Kutta method is used to predict the velocity potential and wave elevation on the free surface. The acceleration potential technique is used to compute the transient wave forces along the wetted object surface. A piston-type wavemaker is used to generate solitary waves. The proposed model is validated by comparing the simulated wave run-up and the wave loads with the published experimental and numerical results of the reflection of a solitary wave from a vertical wall. Then, numerical experiments are performed to study the effects of the narrow gap and the size of each box on the wave run-ups at the two sides of the two-box system and in the narrow gap between two boxes, and the wave loads on the two boxes. The interaction between double solitary waves with a time interval between them with a two-box system is also investigated.

Numerical modelling of nonlinear extreme waves in presence of wind

A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are numerically generated by a piston-type wave maker, and the wind-excited pressure is introduced into dynamic boundary conditions using a pressure distribution over steep crests, as defined by Jeffreys＇ sheltering mechanism.A boundary value problem is solved by a higher-order boundary element method（HOBEM） and a mixed Eulerian-Lagrangian time marching scheme. The proposed model is validated through comparison with published experimental data from a focused wave group. The influence of wind on extreme wave properties,including maximum extreme wave crest, focal position shift, and spectrum evolution, is also studied. To consider the effects of the wind-driven currents on a wave evolution, the simulations assume a uniform current over varying water depth. The results show that wind causes weak increases in the extreme wave crest, and makes the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide a comparison to demonstrate the shifts at focal points, considering the combined effects of the winds and the wind-driven currents.

Numerical Simulation on Hydraulic Performances of Quarter Circular Breakwater

Quarter circular breakwater （QCB） is a new-type breakwater developed from senti-circular breakwater （SCB）. The superstructure of QCB is composed of a quarter circular front wall, a horizontal base slab and a vertical rear wall. The width of QCB＇ s base slab is about half that of SCB, which makes QCB suitable to be used on relatively finn soil foundation. The numerical wave flume based on the Reynolds averaged Navier-Stokes equations for impressible viscosity fluid is adopted in this paper to simulate the hydraulic performances of QCB. Since the geometry of both breakwaters is similar and SCB has been studied in depth, the hydraulic performances of QCB are given in comparison with those of SCB.

Numerical Investigations on Hydrodynamic Performance of An Open Comb-Type Breakwater Under Medium Water Levels

The comb-type breakwater(CTB)has been proposed and investigated in recent years due to its advantages in terms of deep-water adaptability,material saving and water exchanges.All existing empirical formulae for CTBs have been so far restricted to the water level above the bottom of the superstructure,which mainly occurs under the high tides or storm tides.However,based on recent engineering applications and experimental observations,the most severe conditions for CTBs are more likely to occur under a medium water level,because impulsive wave pressure may occur due to interactions between waves and the special chamber in CTBs.Meanwhile,during the most of construction and operation periods,the CTBs are mainly working under the medium water levels,i.e.,water levels below the bottom of the superstructure.In this study,the effects of main influence parameters on the horizontal wave force coefficient and wave transmission coefficient for open CTBs(with partially immersed side plates)under medium water levels were investigated based on a 3D numerical wave flume and corresponding empirical formulae were proposed.It is indicated that the location of the side plate related to the main caisson has significant influence on the hydrodynamic performance of CTBs.In engineering applications,the location of the side plate can be designed at b/L≤0.15 or b/L≥0.3(where b is the distance between the side plate and the front face of the main caisson and L is the incident wave length)for efficiently lowering the horizontal wave force and wave transmission.The flow mechanism of impulsive wave force on CTBs was revealed based on synchronous analyses of flow fields and pressure distribution.Through appropriate design of the height of the superstructure according to H/hD≤1.0 or H/hD≥1.5(where H is the incident wave height and hD is the distance between the still water level and the bottom of the superstructure),the likely impulsive wave pressure on the side plate can also be diminished.

NUMERICAL SIMULATION OF TWO-DIMENSIONAL OVERTOPPING AGAINST SEAWALLS ARMORED WITH ARTIFICIAL UNITS IN REGULAR WAVES

A new mathematical model for the overtopping against seawalls armored with artificial units in regular waves was established. The 2-D numerical wave flume, based on the Reynolds Averaged Navier-Stokes （RANS） equations and the standard κ-ε turbulence model, was developed to simulate the turbulent flows with the free surface, in which the Volume Of Fluid （VOF） method was used to handle the large deformation of the free surface and the relaxation approach of combined wave generation and absorbing was implemented. In order to consider the effects of energy dissipation due to the armors on a slope seawall, a porous media model was proposed and implemented in the numerical wave flume. A series of physical model experiments were carried out in the same condition of the numerical simulation to determine the drag coefficient in the porous media model in terms of the overtopping discharge. Compared the computational value of overtopping over the seawall with the experimental data, the values of the effective drag coefficient was calibrated for the layers of blocks at different locations along the seawalls.

随机风-浪联合传播数值模拟及分析

海洋风、浪往往同时传播,同步传播过程中风、浪之间具有显著的相互耦合作用。针对海洋脉动风和随机波浪同步传播的数值仿真需求,基于程序开发平台MATLAB和计算流体动力学(computational fluid dynamics,CFD)软件平台Fluent,提出了一种随机风场和随机波浪联合传播数值模拟方法,基于该数值方法构建了随机风-浪联合传播数值水槽,并对该数值水槽单独随机风、单独随机波浪以及随机风-浪联合传播的数值模拟效果进行了试算和验证分析。结果显示该水槽数值模拟脉动风速与对应理论计算风速相吻合,水槽数值模拟随机波浪与对应理论计算随机波浪相吻合,水槽风-浪联合数值模拟显示了风、浪之间显著耦合作用效应。建立的随机风-浪联合数值水槽在随机风和随机波浪同步传播的数值仿真上具备可靠性及可应用性。研究内容为海上风、浪环境要素耦合效应研究及海洋工程结构风-浪联合作用相关研究提供了平台基础。

三维数值波浪水槽及其数值模拟验证

波浪水槽能够模拟波浪的产生、传播以及与结构物的相互作用,提供直观、可靠的数据支持。随着计算机技术和数值方法的快速发展,三维数值波浪水槽逐渐成为港口工程领域的研究热点。利用数值模拟软件FLUENT生成三维数值波浪水槽,并结合ANSYS-FSI模块建立三维有限元与有限体积元耦合模型,可以精确模拟波浪作用于斜坡堤等结构上的整个过程。为验证数值模型的准确性,以在波浪作用下斜坡堤顶胸墙的稳定性为例,比较数值模型与理论公式的计算结果。结果表明,数值模型与理论公式的计算结果基本一致,此三维数值波浪水槽模型可靠。在实际工程应用中,可以利用此数值波浪水槽进行方案比选,提升工作效率,同时与物理模型试验结合,共同为港口工程的设计、施工提供有力支持。

WAVE TRANSFORMATION AND BREAKING OVER A RECTANGULAR STEP

An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.

潜堤坡度对波浪传播变形的影响

应用OpenFOAM开源计算平台,基于黏性流理论和有限体积法建立数值水槽模型,系统验证了强非线性波浪的传播及潜堤地形上波浪传播变形的计算准确性和精度,并分析了入射波幅、潜堤坡度等因素对波浪传播特性的影响规律。结果表明:数值水槽模型可较好地模拟强非线性波浪的生成和传播以及波浪经潜堤传播的变形过程;小波陡工况下水面波形具有较好的周期性规律,不同坡度之间存在相位差,具体表现为坡度越平坦,相位越滞后;强非线性波浪条件下,由于波浪破碎,不同坡度波面形态呈现强非线性,水面波形有较大差别;入射波陡由0.53%增大到3.00%的过程中,无量纲化波面的峰谷差均值逐渐减小,体现出潜堤反射作用随着波陡的增大而逐渐增强。

波浪作用下鱼巢型护岸近侧水体动力响应研究

鱼巢型生态护岸可增加岸坡的稳定性、抗冲性,并营造良好的河流生态景观,是当下内河航道常用的护岸形式,而研究波浪作用下鱼巢型护岸近侧水体的动力响应,对护岸工程的设计优化具有重要意义。通过数值模拟与水槽试验相结合的方法,针对不同波况(波高、波角)下鱼巢型护岸所受波浪冲击的变化规律及其周边水体的动压及应力响应特征展开了研究。结果表明:波浪作用下,波高及波角的变化对护岸垂向动压分布形态影响较小;不同波浪入射条件下,护岸侧动压峰值均出现在略低于静水位处(Z=-0.05 m);当入射波高较大时(H=0.10 m),护岸侧的动压整体变大,空腔处对波能的吸收更为明显;入射波角的增大(β=45°)会引起波能分散,使坡面动压峰值减弱。研究成果可为鱼巢型护岸在内河航道防护中的应用提供理论参考。

NUMERICAL WAVE FLUME WITH IMPROVED SMOOTHED PARTICLE HYDRODYNAMICS

This paper presents an improved Nearest Neighboring Particle Searching （NNPS） technique for numerical modeling of water waves with the Smoothed Particle Hydrodynamics （SPH） method. The proposed technique differs from others by introducing the concept of Inner and Outer Particle Searching （lOPS） and shifting most of advanced CPU operations into simple addition operations. The IOPS method is shown to significantly improve the computational efficiency and reduce the CPU time especially for large number of particles, based on comparisons with other two NNPS methods. This method is implemented in a 2DV numerical wave flume conducted by the SPH method. Three test cases are examined, including generations and propagations of dam-breaking induced waves, solitary wave and irregular wave. Calculated results are in good agreements with experimental data and theoretical solutions with fairly satisfactory CPU time-consuming. The wave motions observed in physical facilities are successfully reproduced by the SPH numerical wave flume, revealing its robust capability of modeling realistic wave propagation and substantial potential for a wide variety of hydrodynamic problems.

Propagation and Amplitude Decay Mechanisms of Internal Solitary Waves

In this paper, a modified dynamic coherent eddy model （DCEM） of large eddy simulation is applied to study internal solitary waves in a numerical flume. The model was verified by physical experiment and applied to investigate the potential influence factors on internal wave amplitude. In addition, we discussed the energy loss of internal solitary wave as well as hydrodynamics in the propagation. The results of our study show that （1） Step-depth is the most sensitive factor on wave amplitude for the ＂step-pool＂ internal wave generation method and the wave amplitudes obey a linear increase with step depth, and the increase rate is about 0.4. （2） Wave energy loss obeys a linear decrease with the propagation distance and its loss rate of large amplitude waves is smaller than that of small amplitude waves. （3） Loss of kinetic energy in wave valley is larger than that near the interface due to relative high fluctuating frequency. （4） Discovered boundary jet-flow can intensify the bottom shear, which might be one of the mechanisms of substance transportation, and the boundary layers of jet flows are easily influenced by the adjacent waves.

波浪侵蚀诱发碎石土岸坡变形的模拟试验研究

波浪对岸坡的侵蚀不仅造成水土流失,甚至诱发塌岸和滑坡灾害发生。为探究波浪侵蚀对碎石土岸坡变形的影响,开展了波浪侵蚀岸坡的水槽试验,采用PIV技术对不同侵蚀阶段的岸坡位移进行定量处理,并利用ABAQUS中的“生死单元”功能模拟实现不同阶段的岸坡前缘侵蚀,分析侵蚀进程对岸坡应力场和位移场的影响。研究结果表明:岸坡坡度越大、碎石含量越少,岸坡侵蚀速率越快;水槽试验和数值模拟均表明岸坡后部变形相较于前部变形小,且存在滞后现象,呈现牵引式变形的特征;侵蚀改变了岸坡前缘形态,导致上部土体产生卸荷效应,是岸坡变形的内在原因。