应用时间关联型缓坡方程数值模拟波流相互作用

A Numerical Model for Wave-Current Interactions Based on Time-Dependent Mild-Slope Equation

从含水流项的时间关联型缓坡方程出发,采用有限差分法,建立缓变水深和水流水域波浪传播的数值模型.模型对空间导数项采用三点差分格式离散,对时间导数项采用Euler预测-校正格式离散.基于开边界条件与不同反射特性的固壁边界条件相统一的边界条件表达式,对边界条件进行处理.该模型数值解与椭圆型缓坡方程有限元模型的数值解较为吻合,表明所得数值结果合理可信.

A numerical model for wave propagation in waters of varying depth and current was proposed. This is accomplished by the finite-difference method based on the time-dependent mild-slope equation which incorparates wave-current interactions. In the model, the Euler predictor-corrector scheme is used to discretize the time derivatives, and the three-point finite-difference scheme is used to discretize the spatial derivatives. Based on the general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift, the boundary conditions for the present model are treated. By comparison the numerical solutions with the results obtained from the elliptic mild-slope equation solved by finite element method, it is found to be good. Thus, the present model is capable of giving reasonable numerical resuits.