Numerical Tidal Current Modeling Using Fine Boundary-Fitted Grids for Tidal Flats

Fine grids with small spacing in boundary-fitted coordinates are normally used to treat the computation of fluid dynamics for estuarine areas and tidal flats. However, the adoption of Cartesian components of velocity vectors in this kind of non-orthogonal coordinates will definitely result in a difficulty in solving implicitly the transformed momentum equations, and also complicate the wet-dry point judgement used for flood areas. To solve this problem, equations in terms of generalized contravariant velocity vectors in curvilinear coordinates are derived in the present study, by virtue of which, an Alternative-Direction-Implicit numerical scheme in non-orthogonal grids would then be easily obtained, and wet-dry point judgement would as well be largely simplified. A comparison is made between the explicit scheme and implicit scheme, showing that the present model is accurate and numerically stable for computations of fluid dynamics for estuarine areas and tidal flats.

潮滩海域边界适应网格潮流数值模型

在河口潮滩海域水动力学问题的计算中，为了模拟复杂的地形和岸形，最好采用边界适应坐标和小空间步长的高分辨率计算网格。由此带来的问题是，在非正交的边界适应坐标系中，如果继续采用直角坐标系中的速度分量做为求解未知量，不但给方程组的隐式求解带来困难，而且使潮滩上海水漫滩的干湿格点判断准则变得十分繁琐。本文导出了任意曲线坐标系下普遍适用的速度逆变张量和水位所满足的动力学方程组，从而实现了非正交曲线坐标系下交替方向隐式差分格式，使得在高分辨率的边界适应网格中，仍可采用大时间步长进行计算。速度逆变张量方程的导出同时给潮滩上动边界的实现带来了方便。文中通过数值试验，针对模型的稳定性和精确性与以往显式的适应性网格模型做了详尽的比较研究，从而证实该模型是一种研究河口潮滩动力学问题精确而高效的数值计算模型。

长江口边界拟合坐标的三维潮流数学模型

在正交曲线坐标系下 ,采用坐标变换、有限差分、交替隐式求解、动边界处理等方法 ,建立了边界拟合网格的三维潮流数学模型 .应用在长江口潮流场的计算中 ,得到了与长江口实测潮位、流速和流向相一致的结果 。