基于四叉树网格近海海域波浪、潮流相互作用的数学模型

针对近海岸区域地形、水文、泥沙运动复杂的特点,本文建立了高效的近岸平面二维隐格式潮流、波浪联合作用的数值计算模式.水动力数值模型以非线性的浅水方程为基础,应用Quadtree非结构网格,变量布设采用同位网格,u,v及水位变量布设在同一个节点上,简化计算程序的代码.采用有限体积方法离散方程,应用SIMPLEC程式求解离散的控制方程,由Rhie-Chow的动量插值方法计算界面通量可以避免棋盘式波动.整合的方程组采用最小残差法（GMRES）求解,并利用预条件的不完全Lu分解方法加速其收敛性、提高计算效率.波浪模型以考虑波浪折射、绕射、衍射以及波浪破碎影响的多向不规则波的波作用量守恒方程为基础,计算的波浪幅射应力反应波浪对水体的驱动力.将本文的耦合模型应用到稳态丁坝绕流、理想海湾、法国的Gironde Estuary、波生沿岸流和美国的Grays Harbor算例中,数值模拟结果分别和实验值及测量结果进行比较.计算结果表明,本文建立的平面二维波浪、潮流耦合的数值模型能够准确、高效的模拟复杂计算域的潮流及波浪问题,该模型对近海工程的顺利开展以及海岸带环境保护等方面具有重要的应用价值.

Numerical model of wave-current interaction based on unstructured quadtree grid for nearshore coastal waters

According to the characteristics of complex topography, hydrology, sediment transport in coastal waters, the aim of this paper is to develop an implicit, depth-averaged 2-D numerical mode of coupling current and wave for coastal area. The hydrodynamic model is the two dimensional depth averaged non-linear shallow water equations with an unstructured non-staggered and multiple-level quadtree rectangular mesh with local refinement for important region. In this non-staggered system, primary variables u-, v-velocity, and water level are stored on the same set of grid points in order to simplify the program code, and fluxes at cell faces are determined using the Rhie and Chow＇s momentum interpolation method to avoid spurious checkerboard oscillations. The discretized algebraic equations are solved iteratively using the GMRES method with ILUT preconditioning for speeding the computation. The Wave model is a two-dimensional spectra/wave action model of taking into account the effect of wave breaking, shoaling, refraction, diffraction, wave-current interaction, bottom friction. The wave model readily provides the radiation stresses for the hydrodynamic model. The coupling model has been tested against measurement data for steady flow around a spur-dyke in a laboratory flume and tidal flows in Gironde Estuary, France and Grays Harbor, USA. The model reasonably well reproduces the temporal and spatial variations of water level, current speed and wave height observed in the measurements. It shows that the coupling current and wave model can simulate accurately the questions of tide and wave for complex domain, the modeling approach presented herein should be useful in engineering application and environmental protection for coastal area.