自适应网格在大气海洋问题中的初步应用

自适应网格法是80年代兴起的通过求解椭圆型方程的边值问题来数值生成网格的一种新方法。它是在任意形状的区域上求偏微分方程的数值解的一种非常有效的工具。该方法抛弃了等距均匀的差分网格，代之以能够自动地适应所研究问题中解的特征的疏密程度不均的曲线网格。如在边界上计算网格与实际边界相重合，在区域内部可任意调节网格点的疏密程度等。本文扼要地介绍了自适应网格的原理及其构造方法。并将其应用于生成南海区域的计算网格以及数值预报台风路径的自适应网格。

The Preliminary Application of Adaptive Mesh in the Problems of Atmosphere and Ocean

Adaptive mesh method which raises in 80's is a new method to numerical generate grid by solving a boundary value problem of elliptic equation. It is a very efficient tool to numerical calculate partial differential equations on any shape of domain. Instead of uniformly equidistant difference scheme, it uses nonuniformly curvilinear coordinate system which can automatically adapts the features of the solution, e.g., the calculation grid points at boundary are coincident with actual boundary, and the density of grid points can be adjusted in any subregion and etC. The principle of adaptive mesh and its generation method were introduced in this paper, and applied it to the generation of the computational mesh on the region of South China Sea and the adaptive mesh for the numerical forecasting of typhoon track.