Numerical Simulation Of The Linear Free Surface Condition

This paper presents a numerical simulation method of the linear free-surface condition. This method can he used to calculate the exciting forces and moments acting on an arbitary 3-D body with large flare moving at constant forward speed.By introducing a vertical box shaped surface, which encloses the hull surface in its inner part, the flow field is divided into two parts, known as near field and far field. In the near field, we use simple Green' s function 1/r (Inr), and in the far field, we use time-domain Green' s function. So we can obtain two integral equations of mixed distribution for the velocity potential.In this paper two methods are presented for the simulation of the linear free surface condition. On one hand, with twice-integration of the linear free surface condition with respect to time on the earth-fixed coordinate, we can obtain the integral form of the free surface condition which can also be transformed to get the expression on the translating coordinate. On the other hand, we solve the differential equation of the linear free surface condition, and the corresponding solution can be obtained with some mathematical transform.The computer program is developed to simulate body motion, including 2-D and 3-D bodies without or with forward speed. We are going to especially discuss the influence of free-surface wideness on calculating result.