Calculation Of The Hydrodynamic Forces On A Body Moving In Shallow Water By A NURBS Based High Order Panel Method

When a ship moves in restricted water, the risk of maritime accident, such as collision, striking on the rocks and grounding etc., is larger than the case in unrestricted water. The present standards for ship manoeuvrability promulgated by the International Maritime Organization can not ensure the navigation safety of a ship moving in restricted water, so it is necessary to study the manoeuvring motion and hydrodynamic force of ships in restricted water. As a special case of restricted water, research on manoeuvrability in shallow water is the fundament of that in restricted water. The key of predicting ship manoeuvrability in shallow water accurately is to accurately obtain the hydrodynamic derivatives in manoeuvring motion equations. The method of model tests to obtain these derivatives has some limitations, such as high expense, low efficiency etc. Therefore, it is required to find another more convenient and effective method to obtain the derivatives.Under this background, this thesis has developed independently a high order Rankine panel method based on potential flow theory and Non-Uniform Rational B-Spline (NURBS) for calculating the hydrodynamic force on bodies moving in shallow water. Rankine sources are distributed on the body surface and free surface, whereas a symmetry condition is applied to account for the effect of the sea bottom. A NURBS surface is used to precisely represent the body geometry and free surface. Velocity potential on the body surface is described by B-splines, after the source density distribution on the boundary surface is solved. A collocation approach is applied to numerical computation and the integral equations are evaluated by applying Gauss-Legendre quadrature. A method is developed to deal with the singularity in the numerical computation. In order to verify the numerical method proposed, it is applied to solve the unbounded flow problems of a sphere and spheroids, to calculate the added masses of a spheroid advancing near the wall, to solve the wave-making problems and radiation problems of submerged sphere, submerged spheroid and surface-piercing Wigley hull in deep water, the diffraction problems of submerged sphere and submerged spheroid in deep water, the wave-making problems of submerged sphere and surface-piercing Wigley hull in shallow water, the radiation problem of submerged sphere in shallow water. The numerical results are satisfactory in comparison with the analytical solutions, published experiment results and analytical results. Through a lot of numerical practice, some numerical experiences are accumulated in key technologies relating to the numerical schemes such as arranging mesh, dealing with the free surface, dealing with the singularity problem and so on. These experiences are useful for further development of the panel method for computing the hydrodynamic forces on a ship manoeuvring in shallow water.