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.

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。

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.

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.