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纽曼(Neuman,S.P.)、纳拉辛汉(Narasimhan,T.N.)等人发现,在通常的有限元公式中,由于释放矩阵非对角化所构成的缺点,使得当井流量突然变化时,按通常有限元公式常得出和物理概念有矛盾的水位值。用纳拉辛汉的话来说“是非对角矩阵,会扰动局部质量或能量平衡,虽然在整个区域上仍能保持总的平衡”。纽曼等人后又对无越流项的渗流方程有限元公式进行改进,使释放矩阵对角化后,得出水位值与物理概念相符合。这一工作已被重视,并命名为均衡法。本文的目的,就是将均衡法推广到具有越流项的渗流方程中去。就物理概念而言,这个方法应是局部均衡法。经验表明,利用该方法对地下水进行长期予报比较有效。
Neuman, SP, Narasimhan, TN, et al. Found that in the usual finite element formulation, the shortcomings caused by the non-diagonalization of the release matrix make it possible, when the well flow rate suddenly changes, Finite element formulas often come to conflict with the physical concept of water level values. In the Narathimian phrase, “non-diagonal matrices disturb the local mass or energy balance, although the overall balance is maintained throughout the entire region.” Newman et al. Then improved the finite element formula of the seepage equation without the inflow term to diagonalize the release matrix and concluded that the water level value is consistent with the physical concept. This work has been valued and named as the Balanced Law. The purpose of this paper is to generalize the equilibrium method to seepage equations with over-current terms. In terms of physical concepts, this method should be a local equilibrium method. Experience has shown that it is more effective to apply this method to the long-term reporting of groundwater.