地下水非稳定流的灵敏度分析

发布时间：2018-10-11 11:50

【摘要】：本文主要研究了地下水非稳定流的灵敏度分析问题。首先,陈述推导并且通过计算得到了潜水含水层地下水运动的基本微分方程和二维非均匀多孔介质的控制方程,然后再分析所要求解的边际灵敏度;其次,用伴随法进行非稳定流灵敏度分析。通过对二维非稳定的流控制方程以及它的初始边界条件得出对应的伴随方程,进而解出边际灵敏度,并且讨论了水头关于系统参数(渗透系数和贮水系数)在空间相关和不相关情况下的灵敏度分析;最后,在随机非均匀的多孔介质的矩形域中,用伴随法分别讨论了参数域在空间相关和不相关情况下的灵敏度分析及相应的解析表达式和相关结论。用伴随法对灵敏度进行分析,得到的表达式能更有效的去计算灵敏度,这对模型的分析也是比较有用,此分析方法不仅可以用于地下水方面,还能拓展到其他类似的控制方程和类似概念条件的数学问题中。
[Abstract]:In this paper, the sensitivity analysis of unsteady flow of groundwater is studied. First, the basic differential equation of groundwater movement of the aquifer and the governing equation of two-dimensional inhomogeneous porous media are derived and calculated, then the marginal sensitivity of the required solution is analyzed. The sensitivity analysis of unstable flow is carried out by adjoint method. The corresponding adjoint equation is obtained from the two-dimensional unstable flow control equation and its initial boundary conditions, and the marginal sensitivity is obtained. The sensitivity analysis of the system parameters (permeability coefficient and water storage coefficient) in the case of spatial correlation and non-correlation is discussed. Finally, in the rectangular domain of random non-uniform porous media, the sensitivity analysis of the system parameters (permeability coefficient and water storage coefficient) is discussed. The sensitivity analysis of parameter domain in the case of spatial correlation and non-correlation is discussed by adjoint method, and the corresponding analytical expressions and relevant conclusions are also discussed. By using adjoint method to analyze sensitivity, the obtained expression can calculate sensitivity more effectively, which is also useful for model analysis. This analysis method can be used not only in groundwater, but also in groundwater. It can also be extended to other similar mathematical problems of governing equations and similar conceptual conditions.
【学位授予单位】：成都理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P641.2

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