浅水湖泊群水质模型的近似解析解法

Approximate analytic solution of water quality model for a shallow water lake group

为了实现在一般微机上也能模拟浅水湖泊群的水质变化，从水质变化的基本控制方程出发，根据浅水湖泊群的水流特征与污染物迁移特性，首先建立了浅水湖泊群ＢＯＤ－ＤＯ模型，然后针对恒定水流和污染源稳定排放污水的情形，把处于湖泊边界上的污染源所面临的湖面视为半无限区域，并考虑到浓度的可叠加性，提出了浅水湖泊群ＢＯＤ－ＤＯ模型的近似解析解法。实例结果表明，这种解法计算工作量和存储量都较小，在一般微机上即能进行，且计算准确度基本上能满足工程实际要求。

A shallow water lake group consists of several shallow water lakes connected one after another. Although it has some flow characteristics similar to those in a lake, the outlet status of flow and water quality of any lake among it is the inlet status of the downstream lake, the former has influence upon the later, and its boundary conditions are complex. If the water quality model for a lake group is solved with numerical solutions, not only the boundary conditions are simulated difficultly, but the volumes of calculation and memory will be too large to run at a popular personal computer. In order to simulate the variation of water quality in a shallow water lake group with a personal computer, the plane two-dimensional water quality BOD-DO model for a shallow water lake group has been presented at first in the paper based on the elementary equations of water quality and the characteristics of flow movement and pollutant diffusion and dispersion. Then, as to stable water flow and steady pollutant outflow , an approximate analytic solution has been given to solve the BOD-DO model after having considered the lake water surface where the pollutant outflow located at the lake shore faces as semi-boundless region and the feasibility of density accumulation. It has been shown by the result of the solution that the volumes of calculation and memory are so small that the solution can be run at a personal computer and the calculated results are in line with the measured results.