浅水方程的数值模拟

Numerical Solution to Shallow Water Equation

本文采用拟合坐标系,并用滑动边界条件和弧长不变原理处理边值变换。用破开算子法将浅水方程破开为对流方程和扩散方程,在变换平面上分别用迎风差分格式和有限解析法进行数值计算,所编程序可预报浅水流域的流态及传质传热的对流扩散问题。对两个浅水环流问题进行了计算实践,第一个算例与实验进行了比较,吻合良好。

This paper handles the boundary translation by using the boundaryfitted coordinate system and the method which combines the moving boundary condition with the principle of the constant arc. Using the method of tractional steps, the shallow Water equation is divided into the convection equation and the diffusion equation, which are computed respectively with the upwind difference method and the finite analytic methodon the transformed plane. Two examples about the circulation in shallow water are calculated. The calculation resulti of the first example agrees with the data obtained through experiments.