This study presents a simple, accurate, and efficient method for numerically evaluating the Green function, and its gradient, of the theory of water-wave radiation and diffraction. The method is based on five expressions for the Green function that are useful in complementary regions of the quadrant in which the Green function is defined. These expressions consist of asymptotic expansions, ascending series, two complementary Taylor series, and a numerical approximation based on a modified form of the Haskind integral representation. The four series representations are refinements of the series obtained previously in Noblesse [1].2 These series express the Green function and its gradient as sums of power series and terms involving functions of only one variable. The power series can be evaluated quickly by using recurrence relations; and the functions of one variable, by using rational approximations. The method permits the Green function and its gradient to be evaluated with an absolute error smaller than 10–6 very efficiently (with computing time less than 6 × 10–5 sec on a CDC CYBER 176 computer). A listing of the FORTRAN subroutine is included in the paper.
Three-dimensional water-wave scattering in two-layer fluids
