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Evaluation of wave loads on a ship translating in water waves is of practical importance in ship hydrodynamics, because it is paramount to the design of ship hull structures and provides essential inputs for ship maneuvering analysis. The linear radiation and diffraction of water waves by a translating ship is studied in this paper. A time-domain Rankine panel method is developed in a non-inertial body-fixed coordinate system, which is able to consider large-amplitude horizontal motions consistently. The double-body flow is used as the basic steady flow model. To ensure numerical stability, an implicit Euler scheme is adopted for time marching, and horizontal derivatives on the free surface are calculated using an upwind-biased finite difference scheme. Numerical examples in comparison with experimental measurements are exhibited to demonstrate the validity of the developed solver.

It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present a new 2D Navier-Stokes equation solver based on a recently proposed fourth-order method, namely the generalized harmonic polynomial cell (GHPC) method, as the Poisson equation solver. The GHPC method is a generalization of the 2D HPC method originally developed for the Laplace equation. In the recent development of the HPC method, loss of accuracy on highly stretched or distorted grids has been reported when solving the Laplace equation, while the performance of the GHPC method on non-uniform grids is still not explored and discussed in the literature. Therefore, the local accuracy of the GHPC method is investigated in detail in the present study, which reveals that the GHPC method allows for the use of much larger grid aspect ratio than that for the original HPC method. Global accuracy of the GHPC method on stretched non-uniform girds is also thoroughly analyzed by considering cases with analytical solutions. Obvious advantages of using the GHPC method in terms of accuracy are demonstrated by comparing with a second-order central Finite Difference Method (FDM). The present Navier-Stokes equations solver uses second-order FDMs for the discretization of the diffusion and advection terms, which may be replaced by other higher-order schemes to further improve the accuracy. Meanwhile, an immersed boundary method [1] is used to study the fluid-structure-interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder are studied to confirm the accuracy and efficiency of the new 2D Navier-Stokes equation solver. The predictions show good agreements with the experimental and numerical results in the literature.

As the worldwide oil and gas market continues to grow and environmental concerns with respect to in-port offloading of gas have increased, there has been a boom of interest in new liquefied natural gas LNG terminals in the past years. Loading - offloading operations at LNG and bulk terminals are generally protected by a breakwater to ensure high operability. For these terminals, caisson breakwaters are generally a preferred solution in water depth larger than 15 m due to its advantages compared to rubble mound breakwaters. The caisson installation is generally planned to be carried out in the period where sea conditions are relatively calm. However, many of these terminal locations are exposed to swell conditions, making the installation particularly challenging and subject to large downtime. There is no clear guidance on the caisson installation process rather than contractors’ experiences from different projects/sites. Therefore, studies are required in order to provide general guidance on the range of acceptable wave conditions for the installation operations and to have a better understanding of the influence of the caisson geometry. This paper presents a numerical study to determine the limiting wave conditions for caisson installing operations at larger water depth of 30–35 m for a confidential project along the African coast. Three caisson sizes/geometries are considered in order to assess and compare the wave-structure hydrodynamic interaction. The linear frequency-domain hydrodynamic analysis is performed for various seastates to determine the limiting wave conditions. Viscous effects due to flow separation at the sharp edges of the caisson are considered by using a stochastic linearization approach, where empirical drag coefficients are used as inputs. Parametric studies on caisson size and mooring stiffness are also presented, which can be used as a basis for future optimization. The uncertainty in the applied empirical viscous drag coefficients taken from the literature is examined by using a range of different drag coefficients. Further, the use of clearance-independent hydrodynamic coefficients (e.g. added mass and damping) may be questionable when the caisson is very close to the seabed, due to a possible strong interaction between caisson bottom and seabed. This effect is also checked quantitatively by a simplified approach. The findings of the study are presented in the form of curves and generalized to be used by designers and contractors for general guidance in future projects.

Generally, numerous marine and offshore structures are composed of a number of modules which introduce narrow gaps between the multi-modules arranged side by side. The interaction between water waves and floating structures excites complex wave runup in the gaps and wave forces on the adjacent modules. In this study, free surface oscillations in twin narrow gaps between identical floating rectangular boxes are investigated by establishing a 2D viscous flow numerical wave tank based on a Constrained Interpolation Profile (CIP) method. The Tangent of Hyperbola for INterface Capturing (THINC) method is employed to capture the free surface. The rigid floating bodies are treated by a Virtual Particle Method (VPM). The incident waves are generated by an internal wave maker. For the fixed module cases, the computational results of wave height in narrow gaps are found in good coincidence with the available experimental measurements, especially for the resonant frequencies. The wave forces on the floating bodies are calculated numerically. The characteristic response of wave forces on the leading and rear bodies are consistent with the free surface elevations in the corresponding narrow gaps. With shallow draft, the gap resonance occurs at higher wave number.

The wave-induced responses in the bridge girder of long floating bridges supported by pontoons are often dominated by the vertical modes, coupled horizontal modes and rotational modes about the longitudinal axis of the bridge girder. Pontoons with and without bottom flanges have been seen in recent floating bridge designs. Viscous flow separation around the sharp edges of the pontoon or the bottom flange may have strong influences on the hydrodynamic performance of the pontoon in terms of wave excitation, added mass and damping effects. Morison-type wave and current loads are normally included empirically in the early design phases to account for the viscous effects that cannot be covered by a potential-flow solution alone. Empirical drag coefficients and perhaps a correction to the potential-flow added mass are the inputs to such numerical models, which represents a part of the modelling uncertainties. Previous sensitivity studies using different drag coefficients in the ongoing Bjørnafjord floating bridge project in Norway indicate an influence up to 15% on the maximum vertical bending moment around the weak axis of the bridge girder. This paper contributes to the understanding of viscous effects on the hydrodynamic characteristics, e.g. the added mass, damping and wave excitation loads, of a floating bridge pontoon with and without keel plate. This is achieved by exploring existing model tests for floating bridge pontoons, performing 2D Computational Fluid Dynamic (CFD) analysis for pontoon cross sections and numerical calibration in a simplified frequency-domain model with linearized drag loads. Scale effects are also investigated through CFD analyses in model and full scales.

In this paper, a coupled numerical model in the time domain has been developed to study the interaction between interior liquid sloshing and the motion of a cylindrical closed fish cage when the cage is exposed to regular waves. The single-dominant nonlinear multimodal theory for sloshing in a cylindrical cage presented in [1] was implemented to simulate the liquid responses in the cage. A time-domain simulator based on the Cummins formulation of the equations of motion [2] is used to solve for the cage motion, while WAMIT is used to provide all required frequency-domain hydrodynamic coefficients for the external diffraction/radiation problems. Details of the coupling between cage motion and sloshing will be presented. The coupled solver is verified against the linear frequency-domain solution from WAMIT for the very small wave steepness, where linear theory is valid. The results show that the sloshing effect is a vital factor in the coupling process, which means that the liquid in the closed cage cannot be treated as a solid mass. This is particularly true close to the resonant frequencies of the liquid in the tank. Furthermore, the importance of nonlinearity due to sloshing responses is investigated by applying incident waves with different steepness. When the cage is exposed to regular waves, if certain criteria are met, nonlinear swirling waves are observed in the closed cage. The nonlinear swirling waves are due to the interactions between different sloshing modes, which can only be explained by a proper nonlinear theory, such as the multimodal theory applied in this study. The influence of the swirling waves on the cage motions will also be discussed in the paper. How this effect will impact the design of a closed fish cage and its mooring system can only be answered by studying the cage responses in irregular waves, which is the subject of ongoing research.

A stabilized Higher-Order Boundary Element Method (HOBEM) based on cubic shape functions is presented to solve the linear wave-structure interaction with the presence of steady or slowly varying velocities. The m-terms which involves second derivatives of local steady flow are difficult to calculate accurately on structure surfaces with high curvatures. They are also not integrable at the sharp corners. A formulation of the Boundary Value Problem (BVP) in a body-fixed coordinate system is thus adopted, which avoids the calculation of the m-terms. The use of body-fixed coordinate system also avoid the inconsistency in the traditional perturbation method when 2nd order slowly-vary motions are larger than the linear motions. The stabilized numerical method presented in this paper is based on streamline integration and biased differencing scheme along the streamlines. The presence of convective terms in the kinematic and dynamic free surface conditions will lead to instable solution if the explicit method is used. Thus a fully implicit scheme is used in this paper for the time integration of kinematic and dynamic free surface conditions. In an implicit scheme, solution of an additional matrix equation is normally required due to the fact that the presence of convective terms are approximated using the variables at current time step rather than the previous time steps only. A method that avoids solving such matrix equation is presented in this paper, which will reduce the computational efforts in the implicit method. The methodology is applicable on unstructured meshes. It can also be used in general second order wave-structure interaction analysis with presence of steady or slowly-varying velocities.

To account for the viscous effects of damping devices, for instance, bilge keels or bilge boxes, on the motions of ships and offshore structures, Morison’s equation is often adopted as an empirical but practical approach in the design process. In order to combine the standard engineering panel method with the drag term in Morison’s equation, and remain in the frequency domain, the drag term has to be linearized based on, for instance, stochastic linearization. In this paper, the stochastic linearization scheme is implemented in an in-house code and verified through the comparison with the DNV GL software WADAM. The model test results of a large cylindrical FPSO with bilge box are used to calibrate the drag coefficients in the Morison’s equation. When the linearized drag forces are included, heave motion RAOs correspond better to the model test results. However, the predicted natural periods of heave motions are seen to be smaller than those obtained from model tests. It is suspected that the viscous flow separation around the bilge box increases the added mass of the unit beyond what is predicted by potential flow alone. Discussions are made on the effect of viscous added mass on the heave natural period. It is quite common to only include the damping effects in the motion analysis for large offshore structures and ignore the contribution of the viscous effects on the excitation force. For the considered cylindrical FPSO, this paper demonstrates that the viscous excitation force can be important in survival conditions.

A time-domain Higher-Order Boundary Element Method (HOBEM) based on cubic shape functions for second-order wave-current-body interaction developed by Shao & Faltinsen [1] is further refined by investigating the feasibility of adopting the unstructured meshes on the free surface and body surfaces from an open source mesh generator [2]. When the steady local flow effect is considered in the time-domain boundary-value-problem formulation, the advection terms in the free surface are part of the sources of numerical instability. In this paper, the advection terms are taken care of in an implicit way in a 4th order Runge-Kutta scheme with much better stability. Some numerical examples extensively studied in the literature are studied in order to validate the present numerical model.Copyright © 2014 by ASME

In the Ronald W. Yeung Honoring Symposium on Offshore and Ship Hydrodynamics in OMAE2012 hold in Rio de Janeiro, Shao & Faltinsen [1] have proposed a new numerical 2D cell method based on representing the velocity potential in each cell by harmonic polynomials. The method was named the Harmonic Polynomial cell (HPC) method. The method was later extended to 3D to study potential-flow problems in marine hydrodynamics [2]. With the considered number of unknowns that are typical in marine hydrodynamics, the comparisons with some existing boundary element based methods including the Fast Multipole Accelerated Boundary Element Methods showed that the HPC method is very competitive in terms of both accuracy and efficiency. The HPC method has also been applied to study fully-nonlinear wave-body interactions [1, 2], for example, sloshing in tanks, nonlinear waves over different sea-bottom topographies and nonlinear wave diffraction by a bottom-mounted vertical circular cylinder. However, no current effects were considered. In this paper, we study the fully-nonlinear time-domain wave-body interaction considering the current effects. In order to validate and verify the method, a bottom-mounted vertical circular cylinder which has been studied extensively in the literature will first be examined. Comparisons are made with published numerical results and experimental results. As a further application, the HPC method will be used to study multiple bottom-mounted cylinders. An example of the wave diffraction of two bottom-mounted cylinders is also presented.

Solving potential-flow problems using the Boundary Element Method (BEM) is a strong tradition in marine hydrodynamics. An early example of the application of BEM is by Bai & Yeung [1]. The bottleneck of the conventional BEM in terms of CPU time and computer memory arises as the number of unknowns increases. Wu & Eatock Taylor [2] suggested that the Finite Element Method (FEM) field solver is much faster than the BEM based on their comparisons in a wave making problem. In this paper, we aim to find a highly efficient method to solve fully-nonlinear wave-body interaction problems based on potential-flow theory. We compare the efficiency and the accuracy of five different methods for the potential flows in two dimensions (2D), two of which are BEM-based while the other three are field solvers. The comparisons indicate that it is beneficial to use either an accelerated matrix-free BEM, e.g. Fast Multipole Method accelerated BEM (FMM-BEM), or any field solvers whose resulting matrix are sparse. Another highlight of this paper is that an efficient numerical potential-flow method named the harmonic polynomial cell (HPC) method is developed. The flow in each cell is described by a set of harmonic polynomials. The presented procedure has approximately 4th order accuracy, while its resulting matrix is sparse similarly as the other field solvers, e.g. Finite Element Method (FEM), Finite Difference Method (FDM) and Finite Volume Method (FVM). The method is verified by a linear wave making problem for which the steady-state analytical solution is available, and the forced oscillation of a semi-submerged circular cylinder for which the frequency-domain added mass and damping coefficients are compared. The fully-nonlinear wave making problem and nonlinear propagating waves over a submerged bar are also studied for validation purposes. Only 2D cases are studied in this paper.