The first- and second-order wave-diffraction problems are solved for a submerged cylinder of arbitrary shape by the integral-equation method based on Green's theorem. The integral equation is solved by an element method using cubic splines. The first- and second-order force components, transmission and reflection coefficients are presented for two fifferent contours. The results for the circular contour are compared with experimental results.

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The linear boundary value problem for the wave dynamics inside a tank is very similar to the solution for the outer hull. Because of this, the boundary value solver for the outer hull can be re-used for the tank. The oscillating hydrostatic pressure in the tank may also be calculated in the same way as for the outer hull. Thereby, the hydrostatic coefficients from the tank can also be obtained from the outer solution. This makes it, in principle, easy to adapt outer solution computer code to also account for the inner solutions for all the tanks. The procedure is discussed by Newman (2005). We have used it in a different way, isolating the tank solution into more flexible independent sub-runs. This approach provides part-results for the tanks, like added mass and restoring from the tanks. It also has numerical benefits, with the possibility to reuse the calculations for tanks of equal geometrical shape. We have also extended the procedure to account for full tanks without waves and restoring effects. The linear tank fluid dynamics is programmed into a quite general hydrodynamic frequency domain solver, with the possibility of automatic transferring of local loads to structural (FEM) analysis. Results for local loads are presented. A simpler method of quasi-static loading in tanks is discussed, with comparison to the present method. Effects on global motions and local pressure coming from the tank dynamics contributions are pointed out, such as the shifted resonance of the vessel and the added mass which differs from rigid masses of the tanks.

A time domain Rankine source solver is extended to compute the wave added resistance of ships. The proposed approach applies the momentum conservation principle on the near field fluid volume enclosed by the wet surface of a floating body, the free surface and a control surface. The wave added resistance is then calculated by the integration over the control surface of the fluid velocities and free surface elevations. To be able to incorporate the proposed method with the Rankine source code, an interpolation scheme has been developed to compute the kinematics for the off-body points close to (or on) the free surface. Two Wigley ship models, a containership model S175 and a tanker model KVLCC2 are used to validate the present method. In general good agreement is found comparing with the model test data. The convergence behavior is examined for the proposed method including the selection of the time step and location of the control surface. Both Neumann-Kelvin and double body linearization methods are evaluated with the proposed method. It is found that the Neumann-Kelvin linearization can only be applied for slender ship hull, whereas double body method fits also for blunt ships. It is suggested to apply the proposed method with double body linearization to evaluate the wave added resistance of ships with a control surface close to the ship hull.

Present investigation is based on a numerical study using a time-domain Rankine panel method. The effort and novelty is to extend the applicability of the solver to shallower waters and to steeper waves by including additional non-linear effects, but in a way so to limit the increase in computational costs. The challenge is to assess the improvement with respect to the basic formulation and the recovery of linear theory in the limit of small waves. The wave theories included in the program are Airy, Stokes 5th order and Stream function. By their comparison the effect of the incoming-wave non-linearities can be investigated. For the free-surface boundary conditions two alternative formulations are investigated, one by Hui Sun [1] and one developed here. The two formulations combined with the above-mentioned wave theories are applied to two relevant problems. The first case is a fixed vertical cylinder in regular waves, where numerical results are compared with the model tests by Grue & Huseby [2]. The second case is a freely floating model of a LNG carrier (with zero forward speed) in regular waves, where computations are compared with the experimental results from the EC project "Extreme Seas". This comparison revealed several challenges such as how to interpret/post process the experimental data. Some of these are described in the paper. After careful handling of both computed and measured data the comparisons show reasonable agreement. It is proven that including more non-linear effects in the free-surface boundary conditions can significantly improve the results. The formulation by Hui Sun gives better results compared to the linear condition, but the present formulation is shown to provide a further improvement, which can be explained through the nonlinear terms included/retained in the two approaches. INTRODUCTIONThe basic solver is a well established method for seakeeping problems in finite and deep water conditions with classical corrections for non-linear load terms. The restoring and FroudeKrylov pressures are computed at the instantaneous wetted body surface defined by the rigid body motions and the incident waves. The radiation/diffraction effects are estimated within linear theory, with the corresponding pressures integrated along the mean wetted surface, with the quadratic term in the Bernoulli equation included. The performance of this method has been investigated in several papers, e.g. [3] and [4]. In order to extend the solver to shallow waters and steeper waves, two additional non-linear effects have been included and examined: