FINITE ANALYTIC METHOD FOR MILD-SLOPE WAVE-EQUATION

A difference scheme for the mild-slope wave equation that governs the combined diffraction and refraction of nearshore waves is derived base d on the finite analytic method. The nine-point scheme expresses the v alue of the dependent variable at the central point of a rectangular g rid element as a linear combination of its values at the surrounding n odes. The coefficients of the linear combination depend on the local w ave number as well as the width-to-length ratio of-the grid element an d are approximated, by Taylor expansion, as the polynomials of the rel ative mesh size with coefficients being functions of the width-to-leng th ratio of the grid element. Performance of the scheme is studied by comparing the numerical results with the exact solution for a Dirichle t problem and with the solution by separation of variables for the for ced oscillation in a square basin. The scheme is also applied to the c omputation of wave diffraction by the spherical shoal in a wave channe l, on which carefully measured data in laboratory are available for co mparison.