<p dir="ltr">Numerical investigation of Ocean Brick system is carried out in nonlinear depth NWT, Modified Ocean Brick is proposed to increase the effectiveness of the original Brick. Further numerical simulations are conducted on modified brick.</p>

A 2D fully nonlinear Numerical Wave Tank (NWT) is developed based on the potential theory, mixed Eulerian-Lagrangian (MEL) time marching scheme, and boundary element method (BEM). Nonlinear Wave deformation and wave forces on stationary and freely floating bodies are calculated using the NWT. For verification, the computed mean, 1st, 2nd, and 3rd order wave forces on a single submerged cylinder are compared with those of Chaplin's experiment, Ogilvie's 2nd-order theory, and other nonlinear computation called high-order spectral method. Similar calculations for dual submerged cylinders are also conducted. The developed fully nonlinear NWT is also applied to the calculations of the nonlinear pressure and force of surface piercing barge type structures and these obtained results agree with experimental and theoretical results. Nonlinear waves generated by prescribed body motions, such as wedge type wave maker or land sliding in the coastal slope area, can also be simulated by the developed NWT. The generated waves are in agreement with published experimental and numerical results. Added mass and damping coefficients can also be calculated from the simulation in time domain. For the simulation of freely floating barge-type structure, only fully nonlinear time-stepping scheme can accurately produce nonlinear body motions with large floating body simulations. The acceleration potential method, which was developed by Tanizawa (1996), is known to be the most accurate, consistent and stable. Using acceleration potential method, in the present study, the series of motions and drift forces were calculated over a wide range of incident wave frequencies including resonance region. To guarantitatively compare the nonlinear contribution of free-surface and body-boundary conditions, the body-nonlinear-only case with linearized free-surface condition is separately simulated. All the floating body motions and forces are in agreement with experimental results. Finally, the NWT is extended to fully nonlinear wave-body-current interactions of freely floating bodies, which has not been published in the open literature until now.

This study is to develop a 2D fully nonlinear numerical wave tank used to investigate the wave-induced dynamic properties of a dual pontoon floating structure (DPFS) with a liquid container on the top. The nonlinear numerical wave tank, developed based on the velocity potential function and the boundary element method (BEM), is to simulate dynamic properties including sway, heave, roll, and tension response. In addition, a physical model of the dual floating pontoon is tested in a hydrodynamic wave tank to validate the numerical model for simulation of wave and structure interaction. In the numerical model, a boundary integral equation method (BIEM) with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and a cubic spline scheme. The second-order Stokes wave theory is used to generate the velocity flux on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected waves. Acceleration potential method and modal decomposition method are adopted to solve the unsteady potential functions £X1,t and £X2,t, while the system of motion equation is established according to Newton's 2nd law. Finally, the RK4 is applied to predict the motion of the platform, and the variation of free surface. As for the hydrodynamic laboratory model test, an image process scheme is applied to trace the floating structure motion and the variation of water surface inside the sloshing tank, while the mooring tension is measured by a load cell and stored in a data logger. The comparisons of numerical simulations and experimental data indicate that the numerical predictions are larger than measurements especially near the resonance frequency. This discrepancy is probably due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained through a damping ratio (£a=C/Ccr=0.02) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significantly reduced and close to the measurements. Therefore, the suitable value of the damping ratio for the floating platform is £a=0.02. Then the numerical model with a damping ratio is applied to investigate the dynamic properties of the floating platform for different arrangements, including different mooring angle, spring constant, spacing, and the liquid container. Results demonstrate that the resonant frequency of each mode, responses of body motion and mooring tensions change along with the settings. As a whole, the platform with smaller mooring angle, longer spacing between the pontoons, higher water depth and wider width of the liquid container has relatively stable body motions and less mooring tension. Finally, the comparisons of the effects of random and regular waves on the floating structure illustrate that the variation of water surface in the liquid container is much severe in random waves than in regular waves such that the interaction between liquid and floating structure is more chaotic and thus reduces the amplitude of each response mode. As a result, the mooring tensions for random waves become much gentler than the regular waves. Key words: Boundary integral equation method; fully nonlinear numerical wave tank; dual pontoon floating structure

A 2D fully nonlinear Numerical Wave Tank (NWT) is developed based on the potential theory, mixed Eulerian-Lagrangian (MEL) time marching scheme, and boundary element method (BEM). Nonlinear Wave deformation and wave forces on stationary and freely floating bodies are calculated using the NWT. For verification, the computed mean, 1st, 2nd, and 3rd order wave forces on a single submerged cylinder are compared with those of Chaplin's experiment, Ogilvie's 2nd-order theory, and other nonlinear computation called high-order spectral method. Similar calculations for dual submerged cylinders are also conducted. The developed fully nonlinear NWT is also applied to the calculations of the nonlinear pressure and force of surface piercing barge type structures and these obtained results agree with experimental and theoretical results. Nonlinear waves generated by prescribed body motions, such as wedge type wave maker or land sliding in the coastal slope area, can also be simulated by the developed NWT. The generated waves are in agreement with published experimental and numerical results. Added mass and damping coefficients can also be calculated from the simulation in time domain. For the simulation of freely floating barge-type structure, only fully nonlinear time-stepping scheme can accurately produce nonlinear body motions with large floating body simulations. The acceleration potential method, which was developed by Tanizawa (1996), is known to be the most accurate, consistent and stable. Using acceleration potential method, in the present study, the series of motions and drift forces were calculated over a wide range of incident wave frequencies including resonance region. To guarantitatively compare the nonlinear contribution of free-surface and body-boundary conditions, the body-nonlinear-only case with linearized free-surface condition is separately simulated. All the floating body motions and forces are in agreement with experimental results. Finally, the NWT is extended to fully nonlinear wave-body-current interactions of freely floating bodies, which has not been published in the open literature until now.

This paper is to investigate the wave-induced dynamic properties of the floating platform for cage aquaculture. Considering the calculation efficiency and its applicability, this problem is simplified by: (1) assuming the flow field is inviscid, incompressible and irrotational; (2) the form drag and inertia drag on the fish net is calculated by the modified Morison equation (or Morison type equation of relative motion), including the material and geometric properties; (3) the moorings is treated as a symmetric linear spring system and the influence of hydrodynamic forces on the mooring lines is neglected; and (4) the net-volume is assumed as un-deformable to avoid the inversely prolonging computing time because the mass of fish net with is too light comparing with the mass of floating platform and cause the marching time step tremendously small to reach the steady-state condition which may lead to larger numerical errors (e.g. truncation errors) in computation. The BIEM with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and the cubic spline scheme. The second-order Stokes wave theory is adopted to give the velocity on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected wave energy. The velocity and acceleration fields should be solved simultaneously in order to obtain the wave-induced dynamic property of the floating platform. Thus, both the acceleration potential method and modal decomposition method are adopted to solve the wave forces on the floating body, while the wave forces on the fish net are calculated by the modified Morison equation. According to Newton¡¦s second law, the total forces on the gravity center of the floating platform form the equation of motion. Finally, the RK4 is applied to predict the displacement and velocity of the platform. Firstly, the NWT is validated by comparing the wave elevation, internal velocity and acceleration with those from the second-order Stokes wave theory. Moreover, the numerical damping zone is suitable for long time simulation with a wide range of wave depth. The simulated results on wave-body interactions of fixed or freely floating body also indicate good agreement with those of other published results. Secondly, in the case of the interaction of waves and the floating platform, the simulated results show well agreement with experimental data, except at the vicinity of resonant frequency of roll and heave motions. This discrepancy is due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained by a damping ratio (£i=0.1 ) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significant reduction and close to the experimental data. Moreover, the results are also consistent well with experiments in different wave height, mooring angle, water depth either with or without fish net. Therefore, the suitable value of the damping ratio for the floating platform is £i=0.1. Finally, the present model is applied to investigate the dynamic properties of the floating platform under different draft, width, spacing, spring constant, mooring angle and depth of fish net. Results reveal that the resonant frequency and response of body motion, mooring force, reflection and transmission coefficients and wave energy will be changed. According to the resonant response, the platform with shallower draft, larger width, longer spacing between two pontoons, smaller spring constants, or deeper depth of fish net has more stable body motions and smaller mooring forces. Irregular wave cases are presented to illustrate the relationship with the regular wave cases. Results indicate that the dynamic responses of body motion and the reflection coefficient in irregular waves have similar trend with regular waves. However, in the irregular wave cases, the resonant frequency is moved to the higher frequency. Similarly, resonant response function is smaller but wider, which is due to the energy distribution in the wave spectrum.