利用时域高阶边界元方法建立了模拟极限波浪运动的完全非线性数值模型,其中自由水面满足完全非线性自由水面条件。采用半混合欧拉2拉格朗日方法追踪流体瞬时水面,运用四阶Runge2Kut ta 方法更新下一时间步的波面和速度势,同时应用镜像格林函数消除水槽两个侧面和 底面上的积分。研究中利用波浪聚焦的方法产生极限波浪,并且在水槽中开展了物理模型实验,将测点试验数据与数值结果进行了对比,两者吻合得很好。对极限波浪运动的非线性和流域内速度分布进行了研究。

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.

Boussinesq models describe the phase-resolved hydrodynamics of unbroken waves and wave- induced currents in shallow coastal waters. Many enhanced versions of the Boussinesq equations are available in the literature, aiming to improve the representation of linear dispersion and non-linearity. This paper describes the numerical solution of the extended Boussinesq equations derived by Madsen and Sørensen (Coastal Eng. 1992; 15: 371–388) on Cartesian cut-cell grids, the aim being to model non-linear wave interaction with coastal structures. An explicit second-order MUSCL-Hancock Godunov-type finite volume scheme is used to solve the non-linear and weakly dispersive Boussinesq-type equations. Interface fluxes are evaluated using an HLLC approximate Riemann solver. A ghost-cell immersed boundary method is used to update flow information in the smallest cut cells and overcome the time step restriction that would otherwise apply. The model is validated for solitary wave reflection from a vertical wall, diffraction of a solitary wave by a truncated barrier, and solitary wave scattering and diffraction from a vertical circular cylinder. In all cases, the model gives satisfactory predictions in comparison with the published analytical solutions and experimental measurements.

A fully nonlinear irregular wave tank has been developed using a three-dimensional higher-order boundary element method (HOBEM)in the time domain. The Laplace equation is solved at each time step by an integral equation method. Based on image theory, a new Green function is applied in the whole fluid domain so that only the incident surface and free surface are discretized for the integral equation. The fully nonlinear free surface boundary conditions are integrated with time to update the wave profile and boundary values on it by a semi-mixed Eulerian–Lagrangian time marching scheme. The incident waves are generated by feeding analytic forms on the input boundary and a ramp function is introduced at the start of simulation to avoid the initial transient disturbance. The outgoing waves are sufficiently dissipated by using a spatially varying artificial damping on the free surface before they reach the downstream boundary. Numerous numerical simulations of linear and nonlinear waves are performed and the simulated results are compared with the theoretical input waves.

This paper presents a Cartesian cut-cell Boussinesq model for simulating nonlinear wave interaction with a curved structure. The Cartesian cut-cell technique permits accurate boundary-fitting of complicated, curved geometries in the numerical domain. A Godunov-type shock capturing scheme is used to solve the Boussinesq-type equations in hyperbolic form in order to provide accurate predictions of strongly nonlinear wave interactions with curved structures in shallow water. The numerical model is used to simulate the interaction of a focused wave with a circular cylinder, and excellent agreement is obtained with data from laboratory experiments conducted n a wave basin.

In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall. Based on the image principle, the hydrodynamic problem of a cylinder in front of a vertical wall is transformed into the equivalent problem of double cylinders in unbounded fluid domain. Consequently, an analytical method of eigenfunction expansion is adopted to calculate the radiation of the cylinder due to the motion in surge, sway, roll and pitch, respectively. Moreover, numerical analysis has been carried out in detail in order to discuss the influences of the distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping of the cylinder. It is shown that added mass and damping of the cylinder in front of a vertical wall are evidently different from those in case of the cylinder in unbounded fluid domain from the numerical results. It is also found that the added mass and radiation damping oscillate with wave number, and the oscillating frequency increases with the increasing of the distance between the cylinder and the wall.

A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/ vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.

In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incident waves from four symmetrically arranged circular cylinders, and then the eigenfunction expansion of velocity potential and Grafs addition theorem are used to give the analytical solution to the wave diffraction problem. The relation of the total wave force on cylinder to the distance between the cylinder and orthogonal vertical walls and the incidence angle of wave is also studied by numerical computation.

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(NIg N)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。

高阶边界元法以较常数元方法计算精度高存储低而在工程计算中得到了广泛的应用，但由于其平方存储和计算量的本质，无法应用于大型工程问题中。本文将快速多极子方法(FMM)应用于高阶边界元中从而使其计算量和存储量分别降为O(N log N)和O(N)。通过无限区域中水流绕射算例的数值计算，对FMM高阶边界元法与传统高阶边界元法的运算速度和内存消耗进行了分析对比，结果表明对于大型计算问题FMM高阶边界元算法更加有效。