Yingyi Liu

A calculation method for finite depth free-surface green function

ABSTRACT An improved boundary element method is presented for numerical analysis of hydrodynamic behavior of marine structures. A new algorithm for numerical solution of the finite depth free-surface Green function in three dimensions is developed based on multiple series representations. The whole range of the key parameter R/h is divided into four regions, within which different representation is used to achieve fast convergence. The well-known epsilon algorithm is also adopted to accelerate the convergence. The critical convergence criteria for each representation are investigated and provided. The proposed method is validated by several well-documented benchmark problems.

Numerical investigation of infragravity wave amplifications during harbor oscillations influenced by variable offshore topography

The infragravity (IG) period oscillations inside an elongated rectangular harbor near the offshore fringing reef induced by normal-incident bichromatic short wave groups are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. Based on an IG wave separation procedure, this article presents a systematical investigation on how the maximum IG period component amplitude, the bound and free IG waves, and their relative components inside the harbor change with respect to the plane reef-face slope and the incident short wave amplitude under the condition of the 2nd to the 5th modes. For the given harbor and the ranges of the reef-face slope and the incident short wave amplitude studied in this paper, it is shown that both the maximum IG period component amplitude and the free IG wave component amplitude inside the harbor fluctuate widely with the reef-face slope, and their changing trends with the reef-face slope are almost identical with each other, while the bound IG waves inside the harbor seem insensitive to it. Both the maximum IG period component amplitude and those of the bound and free IG standing waves inside the harbor change cubically with the incident short wave amplitude.

Analytical Study on an Oscillating Buoy Wave Energy Converter Integrated into a Fixed Box-Type Breakwater

An oscillating buoy wave energy converter (WEC) integrated to an existing box-type breakwater is introduced in this study. The buoy is installed on the existing breakwater and designed to be much smaller than the breakwater in scale, aiming to reduce the construction cost of the WEC. The oscillating buoy works as a heave-type WEC in front of the breakwater towards the incident waves. A power take-off (PTO) system is installed on the topside of the breakwater to harvest the kinetic energy (in heave mode) of the floating buoy. The hydrodynamic performance of this system is studied analytically based on linear potential-flow theory. Effects of the geometrical parameters on the reflection and transmission coefficients and the capture width ratio (CWR) of the system are investigated. Results show that the maximum efficiency of the energy extraction can reach 80% or even higher. Compared with the isolated box-type breakwater, the reflection coefficient can be effectively decreased by using this oscillating buoy WEC, with unchanged transmission coefficient. Thus, the possibility of capturing the wave energy with the oscillating buoy WEC integrated into breakwaters is shown.

Numerical study on transient harbor oscillations induced by successive solitary waves

Tsunamis are traveling waves which are characterized by long wavelengths and large amplitudes close to the shore. Due to the transformation of tsunamis, undular bores have been frequently observed in the coastal zone and can be viewed as a sequence of solitary waves with different wave heights and different separation distances among them. In this article, transient harbor oscillations induced by incident successive solitary waves are first investigated. The transient oscillations are simulated by a fully nonlinear Boussinesq model, FUNWAVE-TVD. The incident successive solitary waves include double solitary waves and triple solitary waves. This paper mainly focuses on the effects of different waveform parameters of the incident successive solitary waves on the relative wave energy distribution inside the harbor. These wave parameters include the incident wave height, the relative separation distance between adjacent crests, and the number of elementary solitary waves in the incident wave train. The relative separation distance between adjacent crests is defined as the ratio of the distance between adjacent crests in the incident wave train to the effective wavelength of the single solitary wave. Maximum oscillations inside the harbor excited by various incident waves are also discussed. For comparison, the transient oscillation excited by the single solitary wave is also considered. The harbor used in this paper is assumed to be long and narrow and has constant depth; the free surface movement inside the harbor is essentially one-dimensional. This study reveals that, for the given harbor and for the variation ranges of all the waveform parameters of the incident successive solitary waves studied in this paper, the larger incident wave heights and the smaller number of elementary solitary waves in the incident tsunami lead to a more uniform relative wave energy distribution inside the harbor. For the successive solitary waves, the larger relative separation distance between adjacent crests can cause more obvious fluctuations of the relative wave energy distribution over different resonant modes. When the wave height of the elementary solitary wave in the successive solitary waves equals to that of the single solitary wave and the relative separation distance between adjacent crests is equal to or greater than 0.6, the maximum oscillation inside the harbor induced by the successive solitary waves is almost identical to that excited by the single solitary wave.

An Extremely Efficient Boundary Element Method for Wave Interaction with Long Cylindrical Structures Based on Free-Surface Green’s Function

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters in the coastal region, etc. A higher-order scheme is used to discretize geometry of the structure as well as the physical wave potentials. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss–Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve its computation efficiency, an analytical solution is derived for a fast evaluation of the Green function that needs to be implemented thousands of times. In addition, the OpenMP parallelization technique is applied to the formation of the influence coefficient matrix, significantly reducing the running CPU time. Computations are performed on wave-exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates a good performance of the present method.