潮滩海域边界适应网格潮流数值模型

NUMERICAL TIDAL CURRENT MODELLING USING FINEBOUNDARYFITTED GRIDS IN TIDAL FLATS

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。

Fine grids with small spacing in a boundaryfitted coordinate are normally used to treat the computational problems of fluid dynamics in estuarine area and tidal flats. However, the adoption of the velocity components in this kind of nonorthorginal grids will definitely result in a great difficulty in solving implicitly the transformed momentum equations, thus complicating the wetdry point judgement used in flooding area. To solve this problem, generalized contravariant velocity vector equations in curvilinear coodinates are derived in the present paper, by virtue of which, an AlternativeDirectionImplicit numerical scheme in nonorthoginal grids would then be easily realized, and wetdry points judgement would as well become simple enough. A comparison is made between the explicit scheme and implicit scheme, and the comparison proves the present model to be accurate and numerically stable for the computation in esturine area and tidal flats.