New numerical scheme for simulation of hyperbolic mild-slope equation

The original hyperbolic mild-slope equation can effectively take into accou nt the combined effects of wave shoaling, refraction, diffraction and refle ction, but does not consider the nonlinear effect of waves, and the existin g numerical schemes for it show some deficiencies. Based on the original hy perbolic mild-slope equation, a nonlinear dispersion relation is introduced in present paper to effectively take the nonlinear effect of waves into ac count and a new numerical scheme is proposed. The weakly nonlinear dispersi on relation and the improved numerical scheme are applied to the simulation of wave transformation over an elliptic shoal. Numerical tests show that t he improvement of the numerical scheme makes efficient the solution to the hyperbolic mild-slope equation, A comparison of numerical results with expe rimental data indicates that the results obtained by use of the new scheme are satisfactory.