Numerical solution of Laplace equation for ship problem in the sea using finite difference method

Abstract

In modeling the ocean waves, many equations have been studied widely to model the phenomenon that occurred. One of them is a research about the waves if there is a ship on the surface of the sea. To determine the interaction between the water and the ship (floating structure), the behavior of water needs to investigate. To start the investigation in modeling this problem, we will assume that the ship is a one-dimensional object that is floating on the sea surface. Similarly, we assume that the water flow is uniform in the parallel direction to the ship. Therefore we used the two-dimensional Laplace equation in this problem. In the section that describes the surface of sea, Neuman boundary condition was imposed in part related to the ship and the Dirichlet boundary condition for others. Then on the other three boundaries we imposed the Neumann boundary condition based on its physics. This study was conducted by using finite difference method which determines the velocity potential solution on the whole domain. The result of this study showed velocity potential solution on the whole domain and demonstrated as a result of the implementation of the finite difference method.