Numerical investigation of second-order wave diffraction based on the Rankine source method

作者：Xu, Gang; Duan, Wen Yang^*

来源：Journal of Harbin Engineering University, 2010, 31(9): 1144-1152.

DOI：10.3969/j.issn.1006-7043.2010.09.003

• Artificial boundary condition
• Free-surface boundary conditions
• Integral form
• Multi transmitting formula
• Second orders

In order to exactly predict hydrodynamic forces acting on a floating body, a time-domain second-order method was formulated to simulate a three-dimensional nonlinear wave-body interaction problem. In this approach, Taylor series expansions were applied to the body surface boundary condition and the free surface boundary conditions. The Stokes perturbation procedure was then used to establish a corresponding first and second order boundary value problem on the time-independent surfaces. A boundary element method (BEM), based on the Rankine source, was used to calculate the wave field at each time step. A multi-transmitting formula (MTF) method, with an artificial wave speed, was then employed to satisfy the radiation condition and minimize wave reflections. A stable form, an integral form of free-surface boundary condition (IFBC) was used to update velocity potentials on the free surface. This method was applied to compute uniform flow over a sphere and surface-piercing circular cylinder causing second-order wave diffraction. The numerical precision of the method was then investigated. The results were also compared with analytical solutions and the differences between them were analyzed. It was shown that MTF and IFBC can be used to simulate second-order time domain problems. It was also seen that long-time simulations can be done almost without reflecting waves.

• 出版日期2010
• 单位哈尔滨工程大学