确定任意磁性体磁化方向的样条函数法

由磁异常Z_α和重力异常g,利用样条函数的微、积分性质,从泊松方程出发,直接解得磁性体的磁化方向。该方法适用于任意形状磁性体的磁异常。     

深水中波浪与弱流对结构物的作用

对于深水中波浪和弱流对三维结构物的作用问题,本文提出了一个适用于高阶边界元应用的新的积分方程.基于小流速下格林函数和速度势的摄动展开,本方法避免了移动脉动源的计算,并将未知量限制在物体表面上,使计算速度大为提高,高阶边界元中的不同类型的柯西主值积分,分别采用间接和直接方法加以计算.     

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。     

具有精确色散性的非线性波浪水平二维数学模型

建立具有色散性的水平二维非线性波浪方程,方程的非线性近似到了三阶。方程以波面升高和自由表面速度势表达的微分-积分型数学方程,给出方程的数值求解方法和算例,对方程积分项的处理给出了计算方法。计算结果与Boussinesq方程模型和缓坡方程模型的对应计算结果进行了对比。     

利用有限元方法求解双曲型缓坡方程

本文提出了一种双曲型缓坡方程的有限元计算方法 ,在建立有限元积分方程时通过在造波线处加入脉动源项来实现内部造波 ,并在开边界处利用阻尼层吸波 ,减少了在边界处由于数值处理引起的误差。数值计算结果与实测值吻合良好。本方法可用于大区域波浪场的计算中     

海岸河口三维潮流数学模型

本文采用有限元法建立了适用于海岸河口浅水地区的三维潮流数学模型，垂向采用绝对分层坐标系统，将整个水柱分成若干层，在每层内通过垂向积分平均，将三维问题简化为多个平面二维问题。在求解有限元方程中，引入集中质量矩阵技术，在时间上采用两步ＬａｘＷｅｎｄｒｏｆｆ格式，使有限元方程直接以显式解出，不需联立求解，节省了大量的计算时间和计算内存，通过模拟表面切应力作用在矩形水地上而引起的水流，计算结果与分析解比较一致，并将本模型应用到香港维多利亚水道中，计算结果与实测值亦符合较好，证明本模型是一个实用而有效的三维潮流数学模型。     

波浪与大开孔消浪结构作用非线性数值模拟

基于二维Laplace方程和边界条件,经过Green转换得到以势函数及势函数法向导数为未知量的积分方程。结合0-1混合型边界元和分区边界元方法建立一个适用于求解波浪与大开孔消浪结构相互作用的强非线性波浪变形数值模式,同时给出开孔板上波动压力的计算方法。通过数模与物模结果对比,该数值模式具有较好的精度,可应用于开孔沉箱防波堤消浪效果的计算和研究,其处理原则对其他低反射海工结构物计算也将有适用性。     

关于一类非线性奇异积分方程的可解性

众所周知，解析函数的非线性边值问题与非线性奇异积分方程之间有密切联系，本文将在空间HR，r,δ中讨论非线性奇异积分方程：     

利用海浪谱共轭方程进行东海敏感性区域分布研究

近岸局部范围内的波浪是由远处洋面上生成并传播过来的，它的生成发展源地(敏感性海域)对于所关注范围的波浪起决定性影响。共轭方程中的模式变量反映了物理参量的梯度变化，利用它可以达到精确确定敏感海域具体位置的目的。本文在LAGFD-WAM海浪模式基础上建立了海浪谱共轭方程，提出了通过在关注点邻域加一小扰动作为逆向积分海浪谱共轭方程的驱动项，来计算出梯度极值分布的思想。将这一思想应用于东中国海区域，通过一系列试验来确定舟山及长江口附近海域的敏感性区域位置。试验结果符合物理意义，梯度极值分布结果为下一步的多源卫星观测资料复合分析及最优实测方案设计奠定了基础。     

边界元法应用的进展(二)

三、广义Green公式 当描述物理问题的控制方程不是Laplace方程时,就不可能由Green第二恒等式(2)来建立相应的边界积分表示式了,这时需要采用广义Green公式。 设某个物理问题在以Γ为边界的区域Ω内可由下列偏微分方程描述     

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.     

Simulation of wave power devices

Classical frequency and time domain models of a single degree of freedom wave power device are presented. In the time domain, a convolution integral is conventionally used to represent the fluid dynamic radiation force, characterised by added mass and damping in the frequency domain. This integral is replaced by an approximate ordinary differential equation (ODE) model which is faster and more convenient in simulations. A time domain model of the fluid dynamics of an oscillating water column (OWC) device is derived to illustrate the technique. Digital simulations of the OWC are used to compare the accuracy of the classical and ODE models. The simulation of the ODE model runs about six times as fast as the classical model based on convolution, yet characterises the fluid dynamics accurately.     

A panel-free method for time-domain analysis of the radiation problem

A panel-free method (PFM), based on the desingularized Green’s formulae proposed by Landweber and Macagno, has been developed to solve the radiation problem of a floating body in the time domain. The velocity potential due to a non-impulsive velocity is obtained by solving the boundary integral equation in terms of source strength distribution. The singularity in the Rankine source term of the time-dependent Green function is removed. The geometry of a body surface is mathematically represented by NURBS surfaces. The integral equation can be globally discretized over the body surface by Gaussian quadratures. No assumption is needed for certain degree of approximation of distributed source strength on the body surface. The accuracy of PFM was demonstrated by its application to a classical problem of uniform flow past a sphere. The response function of a hemisphere at zero speed was then computed by PFM. The computed response function, added-mass and damping coefficients are compared with other published results.     

Hydroelastic analysis of cantilever plate in time domain

Numerical solutions for the hydroelastic problems of bodies are studied directly in the time domain using Neumann–Kelvin formulation. In the hydrodynamic part of problem, the exact initial boundary value problem is linearized using the free stream as a basis flow, replaced by the boundary integral equation applying Green theorem over the transient free surface Green function. The resultant boundary integral equation is discretized using quadrilateral elements over which the value of the potential is assumed to be constant and solved using the trapezoidal rule to integrate the memory or convolution part in time. In the structure part of the problem, the finite element method is used to solve the hydroelastic problem. The Mindlin plate as a bending element, which includes transverse shear effect and rotary inertia effect are used. The present numerical results show acceptable agreement with experimental, analytical, and other published numerical results.     

An integro-variational method for interior and exterior free surface flow problems

An integro-variational method is used to solve free surface problems of linear potential flow. Results obtained by the proposed method are compared with solution of the finite element formulation and the boundary integral equation. The I.V. method uses isoparametric element distributed on the contour of the fluid domain.     

Fast computation of the transient motions of moving vessels in irregular ocean waves

A fast time-domain method is developed in this paper for the real-time prediction of the six degree of freedom motions of a vessel traveling in an irregular seaway in infinitely deep water. The fully coupled unsteady ship motion problem is solved by time-stepping the linearized boundary conditions on both the free surface and body surface. A velocity-based boundary integral method is then used to solve the Laplace equation at every time step for the fluid kinematics, while a scalar integral equation is solved for the total fluid pressure. The boundary integral equations are applied to both the physical fluid domain outside the body and a fictitious fluid region inside the body, enabling use of the fast Fourier transform method to evaluate the free surface integrals. The computational efficiency of the scheme is further improved through use of the method of images to eliminate source singularities on the free surface while retaining vortex/dipole singularities that decay more rapidly in space. The resulting numerical algorithm runs 2–3 times faster than real time on a standard desktop computer. Numerical predictions are compared to prior published results for the transient motions of a hemisphere and laboratory measurements of the motions of a free running vessel in oblique waves with good agreement.     

Numerical modelling of wave-structure interaction by a three-dimensional nonlinear boundary element method: A step towards the numerical wave tank

A three-dimensional numerical model for determination of the interaction between non-linear water waves and a structure is developed. The model is based on a boundary integral equation method for the spatial solution of a potential theory problem, combined with a time-stepping method based on the fully non-linear free surface conditions for temporal updating of moments on a structure in the fluid domain. Comparison with experimental results shows good agreement. The present model is considered to be one of the steps towards a three-dimensional numerical model in which the wave-structure interaction in a wave tank can be simulated.     

A coastal ocean model of semi-implicit finite volume unstructured grid

A two-dimensional coastal ocean model based on unstructured C-grid is built, in which the momentum equation is discretized on the faces of each cell, and the continuity equation is discretized on the cell. The model is discretized by semi-implicit finite volume method, in that the free surface is semi-implicit and the bottom friction is implicit, thereby removing stability limitations associated with the surface gravity wave and friction. The remaining terms in the momentum equations are discretized explicitly by integral finite volume method and second-order Adams-Bashforth method. Tidal flow in the polar quadrant with known analytic solution is employed to test the proposed model. Finally, the performance of the present model to simulate tidal flow in a geometrically complex domain is examined by simulation of tidal currents in the Pearl River Estuary.     

高阶边界元方法求解规则波在三维局部渗透海床上的传播

基于线性势流理论,利用高阶边界元法研究了规则波在三维局部渗透海床上的传播。根据Darcy渗透定律推导出渗透海床的控制方程,利用渗透海床顶部和海底处法向速度和压强连续条件得到渗透海床顶部满足的边界条件。根据绕射理论,利用满足自由水面条件的格林函数建立了求解渗透海床绕射势的边界积分方程,采用高阶边界元方法求解边界积分方程进而得到自由水面的绕射势和波浪在局部渗透海床上传播过程中幅值的变化情况。通过与已发表的波浪对圆柱形暗礁的时域全绕射结果对比,证明了本文建立的频域方法计算波幅的正确性和有效性。利用这一模型研究了三维矩形渗透海床区域上波浪的传播特性,并分析了入射波波长、海床渗透特性系数等参数对波浪传播的影响。     

A novel decomposition of the quadratic transfer function (QTF) for the time-domain simulation of non-linear wave forces on floating bodies

In the present study, a novel method is proposed for the separation of the second-order sum- and difference-frequency wave forces—that is, quadratic transfer functions (QTFs)—on a floating body into three components due to wave–wave, wave–motion, and motion–motion action. By applying the new QTF components, the second-order wave forces on a floating body can be strictly computed in the time domain. In this work, the boundary value problems (BVPs) corresponding to the three kinds of QTF components were derived, and non-homogeneous boundary conditions on the free surface and the body surface were obtained. The second-order diffraction potentials were determined using the boundary integral equation method. In the solution procedure, the highly oscillatory and slowly converging integral on the free surface was evaluated in an accurate and effective manner. Furthermore, the application of the QTF components in the time domain was demonstrated. The second-order exciting forces in the time domain were divided into three parts. Each part of these forces was computed via a two-term Volterra series model based on the incident waves, the first-order motion response, and the QTF components. This method was applied to several numerical examples. The results demonstrated that this decomposition yields satisfactory results.