NUMERICAL EVALUATION OF FREE-SURFACE GREEN-FUNCTIONS

A very simple and efficient method for computing the nonoscillatory ne ar-field terms in the expressions for the Green functions, and their g radients, for wave diffraction/radiation by an offshore structure and steady ship waves in deep water is presented. The Green functions are decomposed into three terms corresponding to simple (Rankine) singular ities, wave fields, and nonoscillatory near-field (local) flow compone nts. The method which is presented for approximating the latter nonosc illatory near-field components is based on the use of a coordinate-tra nsformation and a function-transformation. The coordinate-transformati on maps the unbounded domain of definition of the Green function into a finite domain (unit square or cube) of transformed coordinates. The function-transformation expresses the near-field components, which are singular at the origin, in terms of functions that are regular everyw here. Proper coordinate and functin transformations reduce the problem of approximating singular functions in unbounded domains into that of approximating smoothly varying functions within finite domains. The l atter task can be accomplished in a number of ways, including the use of linear table interpolation presented in the study.