多极子去奇异边界元法在三维水波问题中的应用

在众多水波问题，尤其是非线性水波问题求解中，巨大计算量和存储量一直是人们试图克服和解决的重点与难点。本文通过对简单Green函数基本解1／r做多极子展开，并应用到去奇异边界元法中求解三维水波问题。通过无限区域中水流对圆球绕射算例的数值计算，验证了多极子去奇异边界元法能给出高精度的满意结果，与传统边界元方法相比避免了边界积分中奇异性的单独处理并将计算量和存储量均降到了O（NIgN）和O（N）数量级，同时对完全非线性水波问题的时域模拟也得出了令人满意的结果，验证了该方法在处理大计算量问题中所具有的优势。     

应用比例边界有限元法研究波浪与带狭缝三箱作用的共振现象

比例边界有限元法（SBFEM）是一种半解析的新数值分析方法,比完全数值方法具有更高的分析精度.本文应用该方法求解波浪与有限水深中三个相同,但之间存在狭缝的二维固定方箱的作用问题,为波浪与多模块超大型浮体的相互作用提供一些规律。文中给出了各箱的波浪力及反射、透射系数的数值结果,与BEM结果进行了比较,吻合良好.发现波浪与三箱的作用存在双共振现象而且中间箱的共振形式与两边箱不同.进一步分析了箱体吃水深度、狭缝宽度和箱体宽度对三箱共振频率的影响.这对超大型浮体水动力分析和结构设计具有一定的参考价值。数值结果证实该方法用较少单元便能得到精确结果,这为超大型浮体的水动力分析提供了一个可行的分析方法。     

二维时域格林函数的数值计算

本文研究了船舶水动力学问题中二维时域格林函数及其偏导数的算法，并将其表达为与两个基本函数有关的形式，提出了一种快速求取这些函数值的造表插值方法。对于线元上常数源强分布数值模型，发现格林函数偏导数沿线元的积分也可表达为关于上述两个基本函数的解析形式。     

NUMERICAL STUDY FOR NONLINEAR EVOLUTION OF VORTEX SHEET AND ITS APPLICATIONS: PART I. APPROACH AND PERIODICAL EVOLUTION OF VORTEX SHEET

1.　INTRODUCTIONThevortexsheetisaninviscidmodelofaparallelshearflowinwhichthethicknessofthetransitionregionbetweenthetwostreamsissmallcomparedwithatypicalstreamwiselengthscale.Someworkhasbeendonetoinvestigatethevortexsheetevolutionusuallybyusingtwoapproaches.Oneistousesimpleandhigh-orderaccuratenumericalmethodstosolvetheNavier-Stokesequations,andtheotheroneisbasedontheKelvin-Helmholtzinstabilitytheoryandstudiestheinstabilityandevolutionofaninfinitetwo-dimensionalstraightvortexsheetofcons…     

浮式结构物在波浪中的运动响应计算

根据线性波理论和三维源汇分布方法，提供了大尺度浮式结构物在波浪中运动的水动力系数、波浪载荷以及运动响应的计算方法，应用Ｎｅｗｍａｎ的深水Ｒｅｅｎ函数及其数值方法，对于半球、矩形箱式结构物和半潜式平台的考核计算表明，同模型试验结果符合程度是令人满意的。     

波浪力计算中的一个新边界元方法

本文就波浪与结构物作用问题，提出了一个新的高阶边界元方法。较之Ｅａｔｏｃｋ Ｔｏｙｌｏｒ和Ｃｈａｕ的方法，本文在体内附助积分方程中应用了满足刚性水面条件和弱刚性底面条件的简单格林函数。计算速度相应地有所提高；漂浮结构的积分方程更为简洁；计算结果与Ｅａｔｏｃｋ Ｔａｙｌｏｒ和Ｃｈａｕ的方法具有几乎相同的精度和收敛速度。     

AN INTEGRAL EQUATION DESCRIBING RIDING WAVES IN SHALLOW WATER OF FINITE DEPTH

1 .　INTRODUCTIONSmall scalewavessuperposedonlarge scalewavesarecalled“ridingwaves” .Small scalewavesonoceansurfacehasaroused greatinterestwiththegreatimprovementofprecisionofmeasuringinstrumentsusedinthefieldofremotesensing .Thisstudyaimsatunderstandingthemotionofthelarge scalewavesandtheenergyexchangebetweenairandseathroughsomeinformationofsmall scalewaves .Henyeyetal .[2 ] derivedthemotione quationtothefirstorderofridingwavesbyusingacanonicalHamiltonianformulationandassumingsmallwave…     

An iterative Rankine BEM for wave-making analysis of submerged and surface- piercing bodies in finite water depth

A 3-D iterative Rankine Boundary Element Method （BEM） for seakeeping problem in time domain is developed in the framework of linear potential theory. Waves generated by both submerged and surface-piercing bodies moving at a constant forward speed in otherwise calm water, and the resultant steady wave pattern, wave profile and resistance are computed to validate this newly-developed code. A rectangular computational domain moving with the same forward speed as the body is introduced, in which an artificial damping beach is installed at an outer portion of the free surface except the downstream side for satisfying the radiation condition. The velocity potential on the ship hull and the normal velocity on the free surface are obtained directly by solving the boundary integral equation, with the Rankine source used as the kernel function. An iterative time-marching scheme is employed for updating both kinematic and dynamic free surface boundary conditions to stabilize the calculation. Extensive results including the wave patterns, wave profiles and wave resistances for a submerged spheroid and a Wigley hull with forward speed are presented to validate the efficiency of the proposed 3-D time-domain higher-order approach. Finally, the sensitivity of ship-generated waves to the water depth is investigated. Computed results show satisfactory agreement with the corresponding experimental data and other numerical solutions.     

三维数值波动水槽波浪变形计算的0—1混合型边界元方法

为了改善常数元方法和线性元方法在求解三维波场波浪变形问题时的计算精度,考察上述两种单元剖分方式下,波势函数及波势函数法向导数对单元节点设定的适应性,本文构造了一种0—1混合型边界元。计算表明:这种0—1混合型边界元的剖分方式,在控制和减缓波浪“横向振动”幅度及水面单元水质点波动速度的计算方面,显示出了其独到的优越和灵活之处,为时域内的波浪非线性变形计算提供了时步上的数值保证     

TIME-DOMAIN RESPONSES OF IMMERSING TUNNEL ELEMENT UNDER WAVE ACTIONS

The time domain responses of the tunnel element under wave actions during its immersion are investigated based on the linear wave diffraction theory. The integral equation is derived by using the time-domain Green function that satisfies the free water surface condition in the finite water depth, and is solved by the boundary element method. The motion equations of the tunnel element are solved by the fourth order Runge-Kutta method. A comparison between the computed and measured results reveals that the numerical model can effectively simulate the motion responses of the tunnel element and the cable tensions when the motions of the tunnel element are within some limit. Taking the tunnel element of 100 m in length, 15 m in width and 10 m in height as an example, the computational results of the motion responses of the tunnel element and the cable tensions in different immersing depths are obtained under different incident wave conditions.     

随机波浪力连续场的降维模拟

根据水质点的水平速度和加速度过程的功率谱密度,利用线性化的Morison方程,从平稳随机过程自相关函数的角度推导了随机波浪力的功率谱密度函数。在平稳随机过程的源谱表达基础上,通过将标准正交随机变量集定义为仅含1个基本随机变量的正交函数形式,实现了随机波浪力连续场的降维模拟。同时,结合快速傅里叶变换（FFT）技术,给出了随机波浪力连续场降维模拟的快速算法。应用该方法对某一单个小尺度直立圆柱桩所受的随机波浪力进行模拟,给出了随机波浪力过程的均值、标准差、自相关函数及互相关函数等数值特征,并与Monte Carlo方法的结果进行对比分析。研究表明,降维模拟方法具有较高的模拟精度与效率。     

A GIS-ANN-Based Approach for Enhancing the Effect of Slope in the Modified Green-Ampt Model

Most infiltration models survey infiltration in large scale regions using an assumption that the slope of the ground is equal to zero. The Modified Green and Ampt model is one of a few infiltration models that considers slope as an input parameter in its formulation. Here, using artificial neural networks in a raster-based design, basic research is presented regarding the effect of surface slope on infiltration. For the investigation, three catchments with different areas and slopes were selected as case studies, based on existing runoff stations in the upstream region of the Johor River Basin in southern Malaysia. In this research, the efficiency of six different functions was studied in order to determine the best performer for slope in the Modified Green and Ampt model. We also sought to find the most suitable ANN transfer function for infiltration calculations. By calculating runoff for each pixel, accumulation maps were used for corroborating the suitability of the obtained results. The results indicated that the Log-sigmoid was the most appropriate transfer function. We also determined that using the exponential form for the slope in the Modified Green and Ampt model formulation was more accurate, as compared to the original linear shape.     

弯曲管段内流动的大涡模拟

本文应用湍流大涡模拟方法对三维空间的弯管流进行了数值模拟。计算中使用了隐含流线迎风耗散作用具有三阶部分展开的Taylor-Galerkin离散格式，导出了经Gauss滤波流大涡模拟方法适用于边界形状复杂和存在各向异性大尺度涡的流动仿真。     

潜堤上波浪传播过程数值研究

以RANS方程结合Level-Set方法为研究基础,采用五阶WENO有限差分格式进行空间离散、三阶TVD Runge-Kutta格式进行时间推进、Level-Set方法追踪波浪与空气间自由面以及解析松弛法来实现数值水槽中的造波消波,建立了一种求解潜堤上波浪传播问题的数值计算模型。选取经典的潜堤上波浪传播物理试验模型对数值模型进行了验证,水位计算结果与试验值吻合较好。进一步研究了波高、潜堤顶部淹没深度以及潜堤坡度等参数对潜堤上波浪传播过程的影响。结果表明:波高越高、淹没深度越浅、潜堤向波坡度越小,波浪受浅水作用越明显;潜堤背波坡度越小,波浪受反浅水作用稍大,但并不明显。     

ANALYTIC SOLUTION FOR WAVE DIFFRACTION OF A SUBMERGED HOLLOW SPHERE WITH AN OPENING HOLE

An investigation is carried out on the interaction of surface waves with a submerged sphere having an opening hole in finite-depth water in this article. Based on the linear wave theory, the method of multipole expansions is used to obtain the fluid velocity potential in the form of double series of the associated Legendre functions with the unknown coefficients of an infinite set. In terms of the body surface boundary condition and the matching condition between the inner and outer flows at the hole, the complex matrix equations for the coefficients of the series are established. The infinite sets of matrix equations are solved by truncating the series at a finite number. The hydrodynamic pressure on the structure surface and the exciting forces acting on the structure are graphically presented. The dynamic pressure on the wave front surface of the sphere varies slightly with angle of opening hole increasing, while that on the wave back surface does obviously. When the angles of opening hole are increasing, the absolute values of the complex exciting forces tend to fall as a whole.     

变速运动锥体超空泡形状分析与预测

研究了锥体空化器变速运动时非定常自然超空化流问题。基于势流理论,通过在对称轴上分布奇点(源和汇)的方法,建立了变速运动超空泡的积分方程。应用时间有限差分离散化方法,对问题进行了数值求解。分析了锥体空化器在做变速运动时(如速度脉冲变化、加速或减速等),超空泡长度和形状的非定常变化规律。同时,对基于本文方法得到的结果与已有理论的计算结果作了定性比较。本文的分析和预测结果可望为水下航行体空化器的分析与设计起到指导和数据参考作用。     

A NEW NUMERICAL WAVE FLUME COMBINING THE 0-1 TYPE BEM AND THE VOF METHOD

A new coupling numerical wave model, based on both the Boundary Element Method (BEM) and the Volume Of Fluid (VOF) method, is established by taking advantages of the both methods to solve the wave-structure interaction problems. In this model, the wave transformation in front of structures is calculated by the 0-1 type BEM, and the intense wave motions near the structures are calculated by the VOF method. In this paper, the characteristics of the BEM and the VOF method are discussed first, and then the coupling treatments are described in detail. In the end, the accuracy and the validity of the coupling model are examined by comparing the numerical results with experiment results and other numerical results available for the interactions between regular waves with a monolayer horizontal plate.     

不恒定非均匀流场中随机波的折绕射联合数学模型

根据考虑流影响的缓坡方程，运用波动叠加原理，导出了一种适合大范围缓变地形情况下，不恒定非均匀流场中随机波的折绕射联合的数值模式。应用该模式进行了概化的半椭圆斜坡海底及渤海湾西部海域不恒定非均匀流场中随机波传播的折绕射联合的数值计算，获得了比较满意的结果。     

考虑底摩阻损耗的波浪传播与衰减计算的边界元法

边界元法在势流计算中具有使问题降低一维的优点。为了将边界元法与基于粘性流体理论的底部波能损耗结合起来，本文采用一种包含底摩阻系数的底部边界条件，可以在考虑底摩阻损耗的情况下计算极平缓岸坡上波浪的传播与衰减。数值结果得到了物模实验数据的验证。     

基于最小二乘的N-S方程算子分裂有限元法

提出一种新的求解N S方程的有限元法,即基于最小二乘的N S方程算子分裂有限元法。该算法采用算子分裂法将N S方程分解成扩散项和对流项:扩散项时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法;对流项时间离散采用向后差分格式,空间离散采用最小二乘有限元法。应用该算法对方腔流和后台阶流进行数值模拟,方腔流数值计算结果与标准解吻合很好;在后台阶流数值模拟中给出了不同雷诺数下的流场特征和速度对比曲线,所得计算结果与试验结果吻合较好,表明基于最小二乘的N S方程算子分裂有限元法具有较好的收敛性和较高的精度。