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

Advancing ships are numerically modelled in this paper as moving pressure disturbances on the free surface of water. The wave interactions generated by two ships moving in parallel in shallow water were investigated. A Wave Equation Model (WEM) is developed to solve the shallow water equations with moving surface pressure. Galerkin finite element method with moving grids is used to solve a nonlinear second-order wave equation for the free surface elevations and the dynamic pressure of the ship bottom simultaneously. First-order non-reflection condition is enforced on the open boundaries surrounding the ships. Numerical investigations of two moving `Series 60 CB=0.6ʹ ships with streamline-stern or blunt-stern are presented in this paper. Three-dimensional wave interaction patterns are also investigated. It is found that wave interaction occurs mainly behind the ships. Studies of the wave resistance and side force acting on a ship indicate that: (i) the wave resistance decreases due to wave ineraction; (ii) the ships experience an attractive side force when moving parallel in the same direction and (iii) the wave interaction of two blunt-stern ships is stronger than those of the streamline-stern ships at the same initial hydrodynamic speed and conditions.