消除"不规则频率"的非连续高阶元方法

针对使用边界元法计算波浪与结构物相互作用时所出现的“不规则频率”现象，采用连续高阶元和部分非连续高阶元对通过修改积分区域所获得的边界积分方程进行离散，有效地消除了“不规则频率”现象的发生。波浪作用下的截断圆柱所受到的水平波浪力和垂向波浪力的数值计算结果验证了该方法的有效性，同时考虑了非连续单元配置点的选择及单元划分数目对消除效果的影响。     

Edge waves generated by atmospheric pressure disturbances moving along a shoreline on a sloping beach

Edge waves generated by moving atmospheric disturbances parallel to the shoreline are investigated. Following a standard transformation method, an analytical expression of the surface elevation is derived, which consists of an infinite number of modes. Each mode is expressed as the sum of three singular integrals. Using the contour integration method, these singular integrals are converted to regular integrals, which are evaluated by numerical integration methods. The numerical results of two atmospheric pressure distributions studied by Greenspan (1956) are presented, and the resonance conditions are discussed.     

The occurrence of irregular frequencies in forward speed ship seakeeping numerical calculations

This study investigates the occurrence of irregular frequencies in a seakeeping analysis of a ship moving with forward speed. This is achieved by formulating the interior virtual flow Dirichlet or Neumann eigenvalue problem. A theoretical analysis of a rectangular box travelling and oscillating in waves reveals that in the forward speed case, apart from the singular irregular frequency at zero encounter frequency, no irregular frequencies exist whilst at zero forward speed multiple irregular frequencies are observed confirming previous findings. These theoretical predictions are further verified by numerical calculations involving the rectangular box and a Series 60, C_B=0.70, hull.     

Second-order Taylor expansion boundary element method for the second-order wave radiation problem

A novel Boundary Element Method (BEM) named the second-order Taylor Expansion Boundary Element Method (the 2nd order TEBEM) is developed for the solution of the second-order wave radiation velocity potential and sum-frequency wave loads for floating bodies. The radiation condition is enforced by a hybrid method of the multi-transmitting formula and damping zone. For the interior domain problem of a cube and a sphere, numerical results demonstrate that the 2nd order TEBEM can accurately solve the first and second-order gradients of velocity potential on the no-smoothed and smoothed boundary compared to the low-order BEM. The double frequency forces acting on the truncated cylinder are calculated under finite water depth. The agreement between the 2nd order TEBEM and others' numerical results is good. Moreover, all of the singular integrals in the 2nd order TEBEM can be solved analytically, so its implementation is much easier compared to the high-order BEM.     

波浪问题中唯一可解的高阶边界元方法

本文就波浪与结构物相互作用问题，提出了一个适用于高阶边界元应用的新的积分方程，并利用修改积分区域的方法得了适用于本积分方程的不规则频率消除方法。最后，通过数值计算对附加区域的选择、单元的离散做了研究     

Effective boundary element method for the interaction of oblique waves with long prismatic structures in water of finite depth

An effective boundary element method (BEM) is presented for the interaction between oblique waves and long prismatic structures in water of finite depth. The Green's function used here is the basic Green's function that does not satisfy any boundary condition. Therefore, the discretized elements for the computation must be placed on all the boundaries. To improve the computational efficiency and accuracy, a modified method for treatment of the open boundary conditions and a direct analytical approach for the singularity integrals in the boundary integral equation are adopted. The present BEM method is applied to the calculation of hydrodynamic coefficients and wave exciting forces for long horizontal rectangular and circular structures. The performance of the present method is demonstrated by comparisons of results with those generated by other analytical and numerical methods.     

A Higher Order BEM for Wave-Current Action on Structures ——Direct Computation of Free-Term Coefficient and CPV Integrals

1 .Introduction Research on wave action onforward moving bodies or wave-current action on structures is impor-tant in offshore and coastal engineering.For bodies withsimple geometry,analytic solutions have beendeveloped . Matsuiet al .(1991) and Emmerhoff and Sclavounos (1992) derived analytic solutionsforuniformcylinders infinite andinfinite water depth.Bao and Kinoshita (1993) expendedthe theorytotruncated cylinders .In engineering practice ,structures are complexand numerical methods have…     

Spar平台垂荡板水动力系数计算与分析

Spar平台带有厚度很薄的垂荡板,使用边界元方法计算时存在着准奇异积分的数值计算问题。采用自适应高斯积分法对其准奇异积分问题进行处理,较少单元即可达到很高精度。在势流理论下对Spar平台垂荡板的水动力系数进行了计算,并与实验结果进行了对比,发现真实流体中垂荡板的附加质量约为势流理论下附加质量计算结果的1.1倍,而辐射阻尼在总阻尼中所占的百分比很小,此时粘性阻尼成为垂荡板的主要阻尼来源,在工程设计中不可忽略。     

A Unique Solvable Higher Order BEM for Wave Diffraction and Radiation

- For the discretization of higher order elements, this paper presents a modified integral domain method to remove the irregular frequencies inherited in the integral equation of wave diffraction and radiation from a surface-piercing body. The set of over-determined linear equations obtained from the method is modified into a normal set of linear equations by superposing a set of linear equations with zero solutions. Numerical experiments have also been carried out to find the optimum choice of the size of the auxiliary domain and the discretization on it.     

Analysis of hydrodynamic behaviors of gravity net cage in irregular waves

Based on the lumped-mass method and rigid-body kinematics theory, a mathematical model of a gravity cage system attacked by irregular waves is developed to simulate the hydrodynamic response of cage system, including the maximum tension of mooring lines and the motion of float collar. The normalized response amplitudes (response amplitude operators) are calculated for the cage motion response in heave and surge, and the mooring line tension response, in regular waves. In addition, a statistical approach is taken to determine the motion and tension transfer functions in irregular waves. In order to validate the numerical model of a gravity cage attacked by irregular waves, numerical predictions have been compared with the experimental observations in the time and frequency domain. The effect of wave incident angle on the float collar motion, mooring line tension and net volume reduction of the gravity cage system in irregular waves is also investigated. The results show that at high frequencies, the cage system has no significant heave motion. It tends to contour itself to longer waves. The variation amplitude of mooring line forces decreases as the wave frequency increases. With the increasing of wave incident angle, the horizontal displacement of the float collar increases.     

Performance and limitations of the Hilbert–Huang transformation (HHT) with an application to irregular water waves

This paper relates to the newly developed Hilbert–Huang transformation (HHT). An overview of this time-frequency analysis technique and its applications are given. Key elements of the numerical procedure and principles of the Hilbert transformation (HT) are established. A simple parameter study with trigonometric functions to get an idea about the numerical performance of the empirical mode decomposition (EMD) is performed. The main results of estimating relative standardized errors made between analytically exact defined sine waves and disintegrated intrinsic functions as well as their specific influence on each other are determined. Practical applications are carried out next to evaluate computed nonlinear irregular water waves based on Stokes perturbation expansion approach and measurements on fully nonlinear irregular water waves recorded in a laboratory wave flume. Correspondence between simulated and recorded wave trains is given for narrow-banded fundamental components. Deviations are unveiled when carrier and riding waves get broad banded. Time-dependent spectral representation shows signs of an interesting phenomenon as instantaneous frequencies and amplitudes exhibit strong correlations with water surface elevations of both numerical and measured data series.     

数值波浪水槽中完全非线性浅水波仿真特性研究

应用基于势流理论的时域高阶边界元方法,建立一个完全非线性的三维数值波浪水槽,通过实时模拟推板造波运动的方式产生波浪。通过混合欧拉-拉格朗日方法和四阶Runge-Kutta方法更新自由水面和造波板的瞬时位置。利用所建模型分别模拟了有限水深波和浅水波,与试验结果、相关文献结果和浅水理论结果吻合较好,且波浪能够稳定传播。系统地讨论造波板的运动圆频率、振幅和水深等对波浪传播和波浪特性的影响,并对波浪的非线性特性进行分析,研究发现造波板运动频率、运动振幅以及水深均将对波浪形态和波浪非线性产生显著影响。结果为真实水槽造波机的运动控制以及波浪生成试验提供了依据,便于实验室设置更合理的参数来准确模拟不同条件下的波浪。     

Dynamic response of a monopile wind turbine in waves: Experimental uncertainty analysis for validation of numerical tools

The responses of a monopile offshore wind turbine subjected to irregular wave loads are investigated numerically and experimentally, considering a range of sea states. An extensive experimental campaign was carried out on a fully flexible model, representative of a 5 MW offshore wind turbine, at 1:40 scale. An assessment of the experimental results for the response amplitude operator for regular waves and the 90th percentile seabed bending moment in long-crested irregular waves is carried out using two models (analytical and numerical) for uncertainty propagation, suggesting that bias errors in the model properties and in the wave elevation contribute the most to the total uncertainty. The experimental results are also compared to a numerical model using beam elements and Morison-type wave loads with second order wave kinematics. The numerical model does not capture all of the responses within the level of uncertainty of the experiments, and possible reasons for the discrepancies are discussed.     

Second-order coupling of numerical and physical wave tanks for 2D irregular waves. Part II: Experimental validation in two-dimensions

This paper provides an experimental validation of the second-order coupling theory outlined by Yang et al. (Z. Yang, S. Liu, H.B. Bingham and J. Li., 2013. Second-order coupling of numerical and physical wave tanks for 2D irregular waves. Part I: Formulation, implementation and numerical properties, submitted for publication) using 2D irregular waves. This work provides a second-order dispersive correction for the physical wavemaker signal which improves the nonlinear transfer of information between the numerical and physical models compared to the first-order method of Zhang et al. (2007). The important nonlinear parameters and numerical performance were theoretically investigated in Part I. In the present Part II, careful experimental validation is carried out using a sequence of progressively more complex analytical and numerical target waves. The results demonstrate clearly that improved performance is achieved by using the second-order correction. When controlling with a second-order coupling signal, two key points are notable: (i) The higher harmonics underlying the numerical waves are accurately captured and transferred into the physical model. (ii) The second-order behavior leads to an unwanted spurious freely propagating second harmonic that is substantially reduced when compared to an identical wave paddle operating with a first-order coupling signal. Using nonlinear regular (monochromatic), bi-chromatic and irregular wave cases as well as varying coupled wave tank bathymetries, both these aspects are verified over a broad range of wave frequencies and shown to be extensively applicable to physical wave tanks.     

基于HUST-Ship的船舶耐波性数值试验水池参数化建模方法研究

基于自研的HUST-Ship黏性流CFD求解器,提出了一种船舶耐波性数值试验水池参数化建模方法和网格生成技术。在自研的CFD软件平台中,根据波浪参数(规则波的波长、波高和不规则波的特征周期、有效波高)自动生成船舶耐波性数值试验水池。以结构化重叠网格技术为基础,分别对船舶与水池进行网格划分并进行网格的组装、重叠,实现船舶在耐波性数值试验水池中的数值“试验”,对船舶耐波性进行数值预报。根据波浪种类分为规则波数值试验水池与不规则波数值试验水池,可对各类波浪条件实现精确可靠的数值造波,模拟船舶在各种波浪环境中运动响应、耐波性事件与非线性运动特性。采用参数化建模方法生成的耐波性数值试验水池能够提高建模和网格生成效率,通过对国际标模进行数值预报并与船模试验结果对比,验证了参数化建模方法生成的耐波性数值试验水池对船舶在波浪中运动性能的计算精度。     

Variational method for computing surface acoustic pressure on vibrating bodies, applied to transversely oscillating disks

A variational principle derived from the Kirchhoff-Helmholtz integral relation can be applied to acoustic radiation and diffraction problems. An illustrative example discussed here is that of sound radiation from a flat rigid circular disk in transverse oscillation. The variational formulation has the surface pressure as the unknown variable, with the normal velocity of the surface taken as given. The Rayleigh-Ritz method used in determining approximate solutions in terms of truncated expansions of basis functions encounters some numerical problems in the evaluation of integrals with singular integrands. The integrands are nevertheless integrable and techniques are described for handling the singularities. Another potential source of difficulty is that the tangential derivative of the surface pressure for the exact solution must be infinite at the edge of the disk. One makes use of prior knowledge of such a fact by using basis functions with the correct dependence on radial distance near the disk edge. Because basis functions in the Rayleigh-Ritz procedure have been selected with the aid of prior insight into the nature of the true solution, accurate results are obtained with a relatively small number of basis functions. The numerical solutions agree well with results calculated by Leitner in 1949.     

海岸沙坝近底悬移质通量实验研究

为了研究海岸沙坝的产生和演化机理,对不规则波和波群作用下沙坝上方的近底悬移质通量进行了实验研究。分析了短波、长波和平均水流对悬移质通量的影响。结果表明:各种波况下平均水流和长波的作用始终使泥沙向离岸方向输移,而短波的作用使泥沙向岸方向运动;平均水流引起的泥沙输移始终占主要成分,长波的次之。不规则波情况下平均水流的影响较规则波的情况相对较弱,三种成分对泥沙输运的贡献属于同一量级。波群情况下长波的影响随着波浪群性的增强而加大,短波的不明显,而平均水流的影响则随着波浪群性的增强而减弱。     

双色入射波下二阶波浪力响应函数

应用边界元方法,对双频入射波在和频及差频下的二阶速度势做了完整的求解,通过物面积分计算了任意三维结构上的二阶波浪力的传递函数.对简单几何物体,与发表的结果做了对比,两者吻合良好,验证了本方法的正确性.应用这一方法还对复杂的张力腿平台模型做了实际计算,发现在低频和高频区二阶波浪力平方响应函数有着显著的能量分布.     

斜向入反射波分离的数值模拟研究

改进了Goda分离单向入反射波频谱的方法，给出的新方法可应用于斜向入反射波的分离，且测波仪器对的方向可按任意角度布置。当两测点在入射波方向上的投影距离为入射波半波长的倍数时，该方法会出现奇异问题。建议取两测点在入射波方向上投影距离为峰频波长的0．05－0．45倍。这时可得到较好的结果。文中采用数值模拟的方法对模拟波列进行了分离，分离出的波谱与输入的靶谱基本一致，通过分离出的入反射波频谱计算出的各波面过程与输入的各过程线也基本相近，并能较准确地给出结构的反射系数，由此说明该方法是可靠的。     

Simulation of Fully Nonlinear 3-D Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order bouodary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.