Sommerfeld's Radiation Condition Associated with Water Waves and Its Application for Numerical Calculations

Abstract

The water wave problem of oscillating bodies, which has the so-called Sommerfeld's radiation condition on a fictitious boundary placed in a finite distance from a body, is investigated. First, the uniqueness of the solution for the problem is generally demonstrated and the Green function is obtained. Then, making use of this Green function, the solution is shown to approach to that of the original problem when the fictitious boundary tends to infinity, and also, numerical investigation is carried out to estimate the appropriate location of the boundary. Finally, this investigation is examined in the hydrodynamic coefficients of a circular dock computed by the finite element method.