Responding to great concerns about the interaction between steep waves and structures in naval architecture and offshore engineering, a methodology and corresponding numerical algorithm for computing three-dimensional inviscid flow with a free surface are developed based on a fully nonlinear theory in this thesis. The associated boundary value problem is solved using a finite element method. In order to chose an efficient solver for algebraic equations, a direct method and an iterative method with two different preconditioners are compared to each other, which leads to the suggestion that the conjugate gradient method with an SSOR preconditioner is the most suitable for the problem of concern. Furthermore, the radiation condition at a truncated boundary is imposed with an associated damping coefficient optimised to reduce the reflection of waves. In addition, an analytical solution for transient standing waves in a circular tank is derived using second order theory, which provides a tool to validate the numerical method. The developed numerical method is first utilised in simulating the sloshing wave in a tank generated by initial disturbance on the free surface and by the translational motion of the tank. Numerical results are compared with analytical solutions in several cases, which show that the numerical method can be very accurate. The features of the steep sloshing waves are then examined. In the second application, the interaction between vertical cylinders and waves generated by a wave maker is investigated. The motion of the wavemaker can be specified accordingly, in order to generate monochromatic, bichromatic or irregular progressive waves. The forces on one and two cylinders are obtained and compared with published data. The steep waves and their effects on hydrodynamic loads are analysed. It is concluded that the developed methodology based on the finite element method is a good alternative to the existing techniques for the simulation of steep waves. Its accuracy, flexibility and efficiency demonstrated by various numerical examples appear to be quite favourable.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [148]-154).

Thesis (Ph. D.)--University of Washington, 1987. / Vita. Bibliography: leaves [228]-236.

Although extensive work has been carried out on one-dimensional resonant oscillations of both liquids in a tank (where the free surface varies in only one spatial dimension) and gases in a resonator, little is known about two-dimensional solutions. This thesis aims to unite and extend the knowledge about one-dimensional solutions and also develop a theory for classifying two-dimensional motions and, as a consequence, understand the different types of responses that may be found in tanks and resonators of arbitrary geometry. To do this we focus on (i) the nonlinearity and (ii) the geometry (and, hence, the nature of the spectrum) and ignore dissipation to lowest order although it is, in general, important. However, we can easily include dissipative effects a posteriori and its initial absence makes it easier to analyse the new two-dimensional effects. For reasons which will become apparent, we will mainly consider cuboid-shaped geometries and perturb the sidewalls of such tanks and resonators, allowing for the gradual introduction of two-dimensional effects. The thesis is split into two parts, underlying the differences between the problems that arise when the spectrum of the relevant linear problem is commensurate or non-commensurate. After a general introduction in Chapter 1 and a discussion of the model and governing equations in Chapter 2, the first part, comprising Chapter 3, looks at oscillations in deep water where the response typically consists of a finite number of modes. The second part is more extensive, looking at shallow water sloshing and the analogies of this problem with acoustic oscillations, both of which have a spectrum containing an infinite set of commensurate frequencies and the solution is much more intricate. We develop the problem and its one-dimensional solutions in Chapter 4 and then extend these ideas to two-dimensions in Chapter 5. With all this in mind we then make some general remarks about oscillations in tanks and resonators of arbitrary geometry in Chapter 6.

The coupling and interactions between ship motion and inner-tank sloshing are investigated by a potential-viscous hybrid method in time domain. For the time domain simulation of vessel motion, the hydrodynamic coefficients and wave forces are obtained by a potential-theory-based 3D diffraction/radiation panel program in frequency domain. Then, the corresponding simulations of motions in time domain are carried out using the convolution-integral method. The liquid sloshing in a tank is simulated in time domain by a Navier-Stokes solver. A finite difference method with SURF scheme, assuming a singlevalued free surface profile, is applied for the direct simulation of liquid sloshing. The computed sloshing forces and moments are then applied as external excitations to the ship motion. The calculated ship motion is in turn inputted as the excitation for liquid sloshing, which is repeated for the ensuing time steps. For comparison, linear inner-fluid motion was calculated using a 3D panel program and it is coupled with the vessel motion program in the frequency domain. The developed computer programs are applied to a barge-type FPSO hull equipped with two partially filled tanks. The time domain simulation results show reasonably good agreement when compared with MARIN's experimental results. The frequency domain results qualitatively reproduce the trend of coupling effects but the peaks are usually over-predicted. It is seen that the coupling effects on roll motions appreciably change with filling level. The most pronounced coupling effects on roll motions are the shift or split of peak frequencies. The pitch motions are much less influenced by the inner-fluid motion compared to roll motions. A developed program is also applied to a more realistic offloading configuration where a LNG-carrier is moored with a floating terminal in a side-by-side configuration. First, a hydrodynamic interaction problem between two bodies is solved successfully in frequency and time domain. A realistic mooring system, including fender, hawser, and simplified mooring system, is also developed to calculate the nonlinear behavior of two bodies in time domain simulation. Then, the LNG-carrier and sloshing problem are coupled in frequency and time domain, similar to the method in the MARIN-FPSO case. Sloshing effect on LNG-carrier motion is investigated with respect to different tank filling levels including various conditions such as gap distance between two bodies, selection of dolphin mooring system, and different cases of environmental conditions using wave, wind, and current.

In the present study, a fully nonlinear 2-D finite difference scheme has been developed based on inviscid and incompressible flow in a rectangular tank. The rectangular tank is coupled to a linear elastic-supported structure made up by reinforced concrete. Wave breaking and run-up are not considered in the present numerical model due to the free surface is assumed as a single-value function. The main purpose of this study is to analyze interactions between sloshing forces generated by system vibrations and structure motions. The accuracy of present study is made by comparing to other reported numerical results and the consequence shows well agreement. The present study can be applied for designing various combinations of coupled structure systems for different necessity. The analyses of practical examples are also presented in this study. The present numerical model can provide a quick and accurate way on determining the natural frequencies of connecting fluid-structure system and this is hard to identify through experiment.

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Thesis (M.S.)--West Virginia University, 1999. / Title from document title page. Document formatted into pages; contains xi, 80 p. : ill. Includes abstract. Includes bibliographical references (p. 54-55).

Thesis (Ph.D.)--Victoria University (Melbourne, Vic.), 2009.

An interface-preserving level set method is incorporated into the Reynolds- Averaged Navier-Stokes (RANS) numerical method for the time-domain simulation of green water effects. This generalized method can be used to evaluate two- and three-dimensional, laminar and turbulent, free surface flows in moving non-orthogonal grids. In the method, free surface flows are modeled as immiscible two-phase (air and water) flows. A level set function is used to mark the individual fluids and the free surface itself is represented by the zero level set function. The level set evolution equation is coupled with the conservation equations for mass and momentum, and solved in the transformed plane. Chimera domain decomposition technique is employed to handle embedding, overlapping, or matching grids. To demonstrate the feasibility of the method, calculations are performed in several bench mark free surface flows including dam break flows, free jets, solitary wave propagations and the impingement of dam break flow on a fixed structure. The comparisons between the simulations and the experimental data provide a thorough validation of the present method. The results also show the potential capability of level-set RANS method in much more complicated free surface flow simulations. After validations, the method is applied to simulate sloshing flows in LNG tank and green water over the platform. In sloshing flows, the level-set RANS method captures the large impact pressure accurately on LNG tank walls. It also generates a plunging breaker successfully in front of a platform in the numerical wave tank. The good agreements between numerical and experimental results prove the level set RANS method is a powerful and accurate CFD methodology in free surface flow simulations.