平面二维水流-水质有限体积法及黎曼近似解模型

根据研究工程、工业废水及生活污水的水环境影响的需要,提出一个平面二维水流-水质有限体积法及黎曼近似解模型。在无结构网格上对偏微分方程进行有限体积的积分离散,把二维问题转化为一系列局部的一维问题进行求解,模型具备有限单元法及有限差分法两者的优点。由于模型采用黎曼近似解计算水量、动量及污染物输运等通量,不仅提高了数值模拟的精度,而且能模拟包括恒定、非恒定或急流、缓流等水流-水质状态。应用若干理想条件下的精确解对模型精度进行了检验,并结合汉江中下游的水质问题验证了模型的实际应用能力。模型计算结果与精确解拟合极好,与汉江中下游实测的污染分布带也相当吻合,为中线南水北调对汉江中下游水质的影响评价提供了依据。

Finite Volume Method and Riemann Solver for Depth-Averaged Two-Dimensional Flow-Pollutants Coupled Model

A depth-averaged two-dimensional flow-pollutants coupled model is developed to evaluate impacts of industrial effluents and domestic waste on water environment. Developed in the framework of finite volume method on an unstructured grid,the model transfers 2-D problem into solving a series of local 1-D problem. It takes the merits of the finite difference method and the finite element method. The model employs Osher-type approximate Riemann solver to estimate the numerical flux of variables across the interface between cells with high accuracy. The model can be applied to the unsteady and steady stated as well as the subcritical and supercritical flow regimes. The model was examined by several samples with exact solutions. The comparison between computed results and exact solutions demonstrates very good agreement. Finally, the model was applied to water quality simulation in Hanjiang River. The simulated polluted area is matched well with observations.