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In the present work a novel approach has been developed for the resolution of this problem of analysis of the movement of roll of a ship. The methodology used for this is based on the modification of the differential equations of the fluid dynamics (RANSE equations), including the movement of the free surface, by applying the finite calculus method. The modified equations are solved using an implicit predictor-corrector scheme and the finite element method (FEM). This resolution scheme is considered optimal for these types of problems, both in accuracy and in calculation time. As an example, it should be noted that for typical problems (more than 1,000,000 finite elements) less than 4 hours of CPU are required to solve several cycles of ship movement (Pentium IV). This allows the analysis of an array of tests in a few days or even hours, having a computer network or sufficient computing power.

An extension from 2D to 3D of the fully-nonlinear numerical wave tank (NWT) used by Hanssen et al. is presented. Potential-flow theory is assumed, and the high-order harmonic polynomial cell (HPC) field method proposed by Shao and Faltinsen is used to solve the governing Laplace equation for the velocity potential ? numerically. The present work deals with an immersed boundary method without and with the use of an octree technique for local grid refinement near the air-water interface, and examines only wave propagation; dealing with wave-body interactions is planned as a future development.

Skip som opererer ved høye hastigheter utsettes regelmessig for kraftige bølgeinduserte belastninger og vibrasjoner forårsaket av store bevegelser og akselerasjoner. Et neddykket foilsystem kombinert med en kontrollalgoritme for kontroll av skipsbevegelsene er en måte å redusere bevegelsesnivået og størrelsen på disse kreftene. En slik type teknologi kan gi dempning av bevegelsene i det vertikale planet og øke fremoverhastigheten til skipet. Dette fører til en økning av skipseffektiviteten. Reduksjon av uønskede fenomen som ventilasjon og kavitasjon er et annet mulig resultat av foilkontroll. Denne oppgaven undersøker foilkontroll av en valgt høyhastighetskatamaran der et neddykket foilsystem kombinert med en kontrollalgoritme for kontroll av skipsbevegelsene har blitt studert. En høyhastighetskatamaran tidligere brukt av Divisjonen for Marim Hydrodynamikk, NTNU ble valgt for arbeidet. Studiet ble utført i samarbeid med Hydrodynamics, Advisory på DNV GL som har bidratt med prorgramvare og veiledning. En numerisk modell av katamaranen ble laget i HydroD og analysert gjennom lineære hydrodynamiske analyser i Wasim. Geometrien ble validert ved bruk av resultater for en lignenede katamaran funnet i Hydrodynamics of High-Speed Marine Vehicles by Faltinsen. Resultatene ble vurdert som tilfredstillende. Et neddykket foilsystem bestående av fire T-foiler med klaffer kombinert med en relevant kontrollalgoritme ble valgt som konsept. Kreftene forårsaket av foilene ble vurdert teoretisk i tillegg til å bli implementert i den valgte programvaren. Påvirkningen fra foilene på katamaranen ble undersøkt både ved passive foiler med null klaffvinkel, og ved aktive foiler med kontrollerte klaffer. Lineære analyser ble utført i Waqum, og bevegelsene i det vertikale planet ble undersøkt. Det ble sett at det passive foilsystemet forårsaket en signifikant dempning i jag, hiv og stamp. De resulterende hivkreftene og stampmomentene var i 180 grader fase med de respektive hastighetene, noe som gir maksimal dempning. En D-kontroller ble implementert med hovedmål om å redusere stampbevegelsene. Det aktive foilsystemet bidro til en reduksjons-effiktivitets-grad på maksimalt 96%. Stampakselerasjonen ble redusert tilsvarende. I tillegg ble det sett at foilsystemet produserer en positiv horisontal kraft, som bidrar til økt skipseffektivitet. Totalt sett bidrar de kontrollerte foilene til stor nytte for den valgte katamaranen. Due to large motions and accelerations, high-speed vessels regularly experience large wave impact loads and wave-induced vibrations. A submerged foil system together with a ride control algorithm is a measure to reduce the severity of motion and loads. Done correctly, this technology can provide damping of the motions in the vertical plane and increase the vessel thrust, thereby enhancing the efficiency of the vessel. In addition, the foil motion control system can contribute to limiting unwanted phenomena such as ventilation and cavitation. This thesis is a study of the foil motion control of a high-speed catamaran based on investigations of a submerged foil system with a ride-control algorithm. A high-speed catamaran earlier used by the Division of Marine Hydrodynamics, NTNU was selected for the work. The study is executed in cooperation with the Hydrodynamics, Advisory Department at DNV GL, who have contributed both with software and computational tools and guidance. A model of the vessel was created in HydroD, and linear hydrodynamic analyses on the model were run in Wasim. The geometry was validated with results for a similar high-speed catamaran from Hydrodynamics of High-Speed Marine Vehicles by Faltinsen, and was concluded to be satisfactory. A submerged foil system consisting of four T-foils with flaps was selected and investigated, and a relevant control algorithm was selected. Focus was devoted to the theoretical investigation and understanding of the foil loads and the implementation of the foil loads in the selected software. As this thesis combines hydrodynamic theory with control theory, an additional study was executed comparing the computational methods traditionally used in the said disciplines. The influence from the foils on the vessel was investigated both passively, with zero flap angles, and actively, with motion control of the flaps. Linear analyses in regular waves were executed in Waqum, and the motions in the vertical plane were examined. The passive foil system was found to produce significant damping for both the surge, heave and pitch motions and accelerations. The resulting heave force and pitch moment produced by the passive foils was seen to be 180 degrees out of phase with the respective motion velocities, providing maximum damping. A pure D-controller was selected for the final foil motion control, with the main objective of reducing the pitch motion. The active foils provided a reduction efficiency ratio of the pitch motion of 96% at the most, and a corresponding reduction of the pitch acceleration. Heave motion and acceleration were also reduced. The foils were also found to produce a positive horizontal force, increasing the vessel efficiency. Overall, the foil motion control system was seen to be of great benefit for the selected catamaran.

For ocean application, a High Order Spectral (HOS) method is studied. Different from most application of HOS method which use initial value problem to investigate the spectrum evolution, embedded wave generation is implemented to assess the HOS method with the wave tank experiments. The HOS method is also extended for non-uniform bathymetry to handle wave steepening during propagation from deep to shallow water. The enchancement of rogue wave occurence due to bottom topography is studied by considering irregular waves propagation over a sloping bottom. Furthermore, the increasing use of Computational Fluid Dynamics (CFD) in ship and offshore structure analysis requires an accurate water particle kinematics for the input. Therefore, the calculation of water particle kinematics is investigated.