High order numerical code for hyperbolic mild-slope equations with nonlinear dispersion relation

Based on the hyperbolic mild-slope equations derived by Copeland (1985), a numerical model is established in unstaggered grids. A composite 4 th-order Adam-Bashforth-Moulton (ABM) scheme is used to solve the model in the time domain. Terms involving the first order spatial derivatives are differenced to O(Δx)⁴ accuracy utilizing a five-point formula. The nonlinear dispersion relationship proposed by Kirby and Dalrymple (1986) is used to consider the nonlinear effect. A numerical test is performed upon wave propagating over a typical shoal. The agreement between the numerical and the experimental results validates the present model. Biodistribution and applications are also summarized.