Numerical study of wave interaction generated by two ships moving parallely in shallow water

Advancing ships are numerically modelled in this paper as moving pressure d isturbances on the free surface of water. The wave interactions generated b y two ships moving in parallel in shallow water were investigated. A Wave E quation Model (WEM) is developed to solve the shallow water equations with moving surface pressure. Galerkin finite element method with moving grids i s used to solve a nonlinear second-order wave equation for the free surface elevations and the dynamic pressure of the ship bottom simultaneously. Fir st-order non-reflection condition is enforced on the open boundaries surrou nding the ships. Numerical investigations of two moving 'Series 60 C-B = 0. 6' ships with streamline-stern or blunt-stern are presented in this paper. Three-dimensional wave interaction patterns are also investigated. It is fo und that wave interaction occurs mainly behind the ships. Studies of the wa ve resistance and side force acting on a ship indicate that: (i) the wave r esistance decreases due to wave ineraction; (ii) the ships experience an at tractive side force when moving parallel in the same direction and (iii) th e wave interaction of two blunt-stern ships is stronger than those of the s treamline-stern ships at the same initial hydrodynamic speed and conditions . (C) 2001 Elsevier Science B.V. All rights reserved.