Numerical analysis of free surface flow around a ship in deep water

Abstract

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A boundary element method is presented for solving a non-linear free surface flow problem for a ship moving with a uniform speed in deep water. The free surface boundary condition is linearized by the systematic method of perturbation in terms of a small parameter. The surfaces are discretized into flat quadrilateral elements and the influence coefficients are calculated by Morino’s analytical formula. Dawson’s upstream finite difference operator is used in order to satisfy the radiation condition. The method of solution is based on the distribution of sources and dipoles on the body and the free surface, which will be obtained by a matrix solution. The matrix is solved by the L-U decomposition method. A verification of the numerical modelling is made using the Wigley hull and validity of the computer program is examined by comparing the details of wave profiles and wave-making resistance with the experimental result. The wave pattern consisting of transverse and diverging waves around ships in deep water is well predicted numerically.

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