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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。
According to the need of research on the influence of water environment of research project, industrial wastewater and domestic sewage, a two-dimensional planar flow-water finite volume method and Riemann’s approximate solution model are proposed. Finite volume integral discretization of PDE is done on unstructured grid, and the 2D problem is transformed into a series of local one-dimensional problems for solving. The model has the advantages of finite element method and finite difference method. Because the model uses the Riemann approximation solution to calculate the flux of water, momentum and pollutant transport, it can not only improve the accuracy of numerical simulation, but also simulate the flow-water quality including constant, unsteady or rapid and slow flow. The accuracy of the model was tested by using exact solutions under several ideal conditions. The practical application ability of the model was verified with the water quality in the middle and lower reaches of the Han River. The results of the model are well fitted with the exact solutions, which are also in good agreement with the measured pollution distribution bands in the middle and lower reaches of the Han River. This provides a basis for evaluating the impact of the midline SNW on the water quality in the middle and lower reaches of the Han River.