摘要
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。
Mass conservation is the basic requirement for a mathematical model of transport.However,the problem of non-conservation of mass was found in the 1-D scalar transport model for river-networks originally developed by domestic researchers.A corrected 1-D scalar transport model for river-networks,which fulfills the requirement of mass conservation,was proposed on basis of corrections of the original 1-D model.Mass conservation of the corrected model was tested subsequently.Study shows that the cause of the problem of non-conservation of mass in the original 1-D model is basically related to the inappropriate setup of its variable （concentration of substance）,which is defined at the cross-sections rather than the center of control volumes in model segments.The inappropriate setup brings on the problem of non-conservation of mass during the period when the water flow direction is changing or the water flow from both sides of a model segment to its middle.In addition,the tests for mass conservation indicate that the corrected 1-D model is capable of fulfilling the requirement of mass conservation in the simulation.
出处
《水动力学研究与进展（A辑）》
CSCD
北大核心
2010年第3期337-343,共7页
Chinese Journal of Hydrodynamics
关键词
感潮河网
一维物质输移模型
质量不守恒
修正
tidal river-network
1D scalar transport model
non-conservation of mass
correction
