Fundamental Studies on Steady Ship Wave Problems by the Finite Element Method (The Second Report)

Abstract

Finite element formulations have been proposed by several authors for solving linear water wave problems. Seto and the senior author proposed a finite element technique called the method of superposition, taking advantage of the linearity of the governing equations and the asymptotic behaviors of solutions at infinity : The water field is divided into two parts, outer and inner domains, by a fictitious surface, and it is assumed that the outer solution is obtained analytically within a certain number of unknown parameters. The inner solution is determined by the finite element method, and the unknown parameters in the outer solution are determined by the continuity condition on the fictitious surface.In the present paper, the authors study practical techniques for applying this method to infinitely deep water fields, for which the finite element method encounters some difficulties. Introducing the secondary fictitious surface, and modifying the bottom boundary condition, the authors obtain good approximations with simple analytical solutions as the outer solutions.Moreover, an input generator program is discussed. Dependency of hydrodynamical force coefficients on form approximation for ships is investigated with numerical examples.