The Simulation Study Of Wave Propagation On Reefs Terrain Based On Numerical Model Of Mild-Slop Equation

When the waves propagate from the deep water to the inshore reefs, generally a large gap reef flat must be overcome, leading to dramatic changes in water depth. This will cause the wave breaking. It is important for the engineering design on the terrain to accurately simulate the wave breaking and calculate the wave heights after wave breaking.Mild-slope equation is one of the best numerical models to describe nearshore wave transformation. So based on Berkhoff elliptic mild slope equation and a series of boundary conditions, and adopting finite element method, a new preconditioning program which can obtain optimal meshes in terms of different bathymetry and wave length can be developed in this paper.In order to reduce the storage requirement and save computer expense, the index-storage method and conjugate gradient method are employed to solve the large sets of simultaneous equations. Moreover, the prior error estimation, Z2 posterior error estimation and an adaptive remeshing method based on the h-method are used to improve numerical accuracy.Based on a self-adaptive finite element numerical model to solve the mild-slope equation, a nearshore numerical model to simulate wave breaking is developed by introducing the wave breaking model in this paper. Four kinds of wave breaking model are used and compared based on the experimental results of the wave propagation on the two-dimensional reefs terrain. A numerical model for solving the regular wave transformation on the two-dimensional reefs terrain is proposed. And the effectiveness of the model is verified again by the simulation of irregular wave breaking.Moreover, based on the effectiveness on the two-dimensional reefs terrain, the advantage and disadvantage of the model on a three-dimensional reefs terrain in South China Sea are verified. And the practical range is proposed, which can provide some help to the engineering design on the terrain.