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质量守恒是数学模型的基本要求。然而,国内一些较为广泛应用的一维河网物质输移模型却存在明显的质量不守恒问题。本文在分析该问题产生原因的基础上,对原模型提出了修正,进而建立满足质量守恒的一维河网物质输移模型,并对修正后的模型进行质量守恒检验。研究结果表明,原模型产生质量不守恒问题的根本原因在于模型的求解变量(物质浓度)定义于河段断面上,而非河段控制体中心,这一不当的设置导致模型在水流转向或者顺逆流的情况下出现质量不守恒的现象;质量等恒测试结果显示,修正后的模型成功解决了原模型质量不守恒的问题,其在计算过程中能够保证质量守恒。
Conservation of mass is a basic requirement of mathematical models. However, some of the more widely used models of 1D river network material transport have obvious problems of non-conservation of mass. Based on the analysis of the cause of the problem, this paper proposes a revision of the original model, and then builds a one-dimensional river network mass transport model that satisfies the conservation of mass and tests the modified model for conservation of mass. The results show that the root cause of the problem of non-conservative mass in the original model is that the model’s solution variable (material concentration) is defined on the section of the river, not on the center of the control body of the river. This improper setting causes the model to change direction In the case of countercurrent flow, the phenomenon of non-conservation of mass occurs. The constant test of mass shows that the modified model successfully solves the problem of non-conservation of mass of the original model and guarantees the conservation of mass during the calculation.