有限单元法模拟地下水流的水头反常现象——对流量计算的作用

地下水流数值模拟是定量研究地下水水量和水质的重要手段。为揭示有限单元法水头反常现象形成的原因,以三维非均质模型为例,刻画了水头反常现象。储量集中法(Lumped Mass方法)是有限单元法中储释水量计算的替代算法,可以改善水头反常现象。对结点控制区域的均衡性质进行了研究,分析了使用Lumped Mass方法时的水头反常现象,结果表明:结点控制区域的对流量计算受到该结点所在层及其相邻层水力坡度的影响;在抽水初始阶段,抽水井结点水头快速下降,导致相邻层中相邻结点控制区域的侧向流入量为正值,控制区域为储水过程,结点水头上升,表现出水头反常现象。因此,有限单元法中对流量的计算是引起水头反常现象的原因。

Abnormal waterhead phenomenon in groundwater flow simulation by using the finite element method: caused by the computation of advection fluxes

Numerical simulations are an important tool for quantitative research on the volume and quality of groundwater. To reveal the cause of an abnormal waterhead phenomenon using the finite element method, a three-dimensional inhomogeneous model is applied as a case study. The Lumped Mass method is an alternative approach for computing storage changes, which can be used to ameliorate abnormal waterheads. In this paper, the Lumped Mass method is applied to an abnormal waterhead phenomenon by analyzing the local conservation. It is observed that the advection fluxes in the control domain of a vertex refer to the hydraulic gradients in that slice and in adjacent slices. As water starts to be pumped, the potential of the well vertex decreases rapidly. This leads to a positive flux flowing into the control domain of an adjacent vertex in an adjacent slice. The storage change of the control domain in this adjacent vertex is positive, and so the potential increases. Hence, the computation of advection fluxes in the finite element method is the cause of the abnormal waterhead phenomenon.