A numerical method for two-dimensional studies of large amplitude motions of floating bodies in steep waves

Sen, Debabrata (1988) A numerical method for two-dimensional studies of large amplitude motions of floating bodies in steep waves. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

A numerical time-domain method is developed to simulate large-amplitude motions of two-dimensional floating bodies in steep waves. The method employs an integral relation derived from Green's second identity and a discretization scheme of centrally located collocation points on linear boundary segments for solution of the full non-linear potential flow problem. Propagating unsteady waves are simulated by imposing an Airy wave potential as a source of excitation on a hypothetical vertical boundary of a rectangular fluid domain. Solutions of linearized wave-propagation problems are in very good agreement with analytical solutions. For the non-linear problem, an Eulerian description of the free surface is used in which vertical movements of the collocation points on the free surface are followed. Smoothing schemes in space and time at the upstream boundary, intermittent smoothing of the free surface and adaptation of a numerical radiation condition permit modelling of very steep progressing waves over 20 wave periods. Numerical experiments reveal insignificant degeneration of the solution resulting from the embodied techniques. The effectiveness of the method is further illustrated by its application to a study of steep waves interacting with vertical walls. Comparison with experimental and analytical results demonstrates the capability of the method in accomplishing non-linear steady state solutions with very good quality of agreement with experimental data. -- In the study of behaviour of floating bodies in steep waves, numerical instability leads to failure of the simulation scheme unless special care is taken with regard to the discretization and treatment of the coupled force-motion relation. The motion of the body with respect to the free surface may result in large variations of the spatial grid sizes in the vicinity of the body and the free surface intersection, which results in destabilizing force effects through the computation of the linear dynamic pressure term (dϕ/dt). These difficulties are resolved by means of an appropriate spatial regridding scheme, and by employing a central difference rule for computation of the dϕ/dt term at the corrector level of the adopted Adams-Bashforth-Moulton rule in the time-integration scheme and by utilizing explicit rules for integration of the equations of motion. A number of computations simulating motions of a rectangular floating body in different situations provides evidence of the efficacy of the algorithm. The presented results contain large roll and heave motions as well as drifting behaviour of a completely unrestrained body. -- A complementary experimental study is also described, in which a rectangular body of rounded-off corners restricted from swaying was subjected to wave excitations inside a channel. Comparison of experimental and computational results shows in general very good agreement over the entire range of the tested conditions, inclusive of resonant behaviour in heave and moderately large roll motions. For this latter behaviour, accounting for viscous effects by means of a semi-empirical procedure improves the correlation significantly.

Item Type: Thesis (Doctoral (PhD))
URI: http://research.library.mun.ca/id/eprint/11398
Item ID: 11398
Additional Information: Bibliography: leaves 334-349.
Department(s): Engineering and Applied Science, Faculty of
Date: 1988
Date Type: Submission
Library of Congress Subject Heading: Fluid dynamics; Navier-Stokes equations; Water waves--Dynamics.

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