Abstract
By assuming that the velocity potential is locally represented by a polynomial analytically satisfying Laplace's equation, a method is developed to compute the evolution of surface gravity waves over varying topography for one dimension in plan. This local polynomial approximation (LPA) method is fast and simple and has no essential approximations in its treatment of the free surface boundary conditions. Different degrees of approximating polynomial may be used, which makes the method highly flexible. Conservation of energy considerations and comparison with both analytic results and experimental data show that, with the right choice of parameters, almost any desired level of accuracy may be achieved.
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