A simple method to solve potential flow problem of submerged body-surface wave interaction is presented. The equation governing flow below the surface is Laplace equation. The boundary condition on the body is of Neumann type, while on the free surface the nonlinear dynamic free surface condition has to be satisfied. In addition, farfield and radiation condition, which determine the behavior of wave going to infinity, have to be satisfied. Taking advantage of potential flow model, then Green Identity is used to transform the problem of Laplace equation with nonlinear boundary condition into "a nonlinear problem in its boundary. To satisfy the nonlinear dynamic free surface condition, Newton iteration is employed. The scheme for relaxation is obtained by expanding the nonlinear dynamic free surface condition obtain correction terms to the velocity potential. Truncation up to linear terms results in a simple scheme. Since the dynamic condition is valid on the unknown location of the free surface, in each iteration step the position of the free surface where the equation is applied, is corrected using Bernoulli equation. In this manner, dynamic free surface condition is satisfied exactly at the collocation points. Results for two and three dimensional nonlifting problem are presented as examples.
The problem of submerged body-surface wave interaction is relevant in many practical applications, such as in the prediction of the forces when the body is subject to certain flow conditions in the design of off-shore structures and ship hulls. Of great interest is the drag component attributed by the free surface wave induced by the motion of the submerged structure. The resistance of a body experiencing relative motion with respect to the otherwise undisturbed flow comprises two components, viscous and wave resistances, which may be assumed to be independent of each other (Berg Raven and Valhof, 1990).
