近岸波浪传播的非静压数值模型

A non-hydrostatic model for water waves in nearshore region

基于均匀网格,建立了沿水深积分的非静压波浪传播数值模型,模型的求解分静压步和动压步两部分。静压步的控制方程为全非线性浅水方程,采用有限体积格式求解,通过采用线性重构技术和全隐式离散底摩阻项,保证了格式的和谐性、守恒性和水深非负性,有效处理了海岸动边界问题。动压步通过应用有限差分方法求解泊松方程考虑动压力,使得模型具备模拟色散性波浪传播的能力。引入波浪破碎指标,波浪破碎后模型退化为静压模型,破碎波自动捕捉为间断。通过算例对所建立模型进行了验证。

Based on uniform grid,a depth integrated non-hydrostatic model for coastal water flow is presented. The numerical implementation of the model is split into hydrostatic step and non-hydrostatic step. In the hydrostatic step,an efficient finite volume scheme is used to solve the fully nonlinear shallow water equations,where the hydrostatic reconstruction approach and the implicit treatment of the bottom friction are used to ensure the properties of well balance,conservation and non-negative water depth,and moving shoreline is also efficiently handled. In the non-hydrostatic step,the predicted solutions from hydrostatic step are corrected by the contribution of the dynamic pressure,which is obtained by solving Possion equations using finite difference method. A simple criterion is introduced to identify breaking waves and the governing equations are then switched off to the fully nonlinear equations,which admit breaking waves as a shock. Some numerical tests are conducted for model validation.