Interstitial Water Transport Model in Aquifer Systems by Finite Element Method

摘要

A finite element method is described for the solution of the Richards' equation governing the groundwater flow in variably saturated porous media. The dependent vairable, the pressure head, is approximated over each isoparametric element using mixed linear, quadratic, and cubic base functions. This approximation reduces the problem to a set of matrix equations whose term associated with the temporal derivative is the mass matrix. The lumping of the mass matrix together with the application of explicit time integration schemes produces an efficient method of solution. Because of the elliptic nature of the Richards' equation in spatial dimensions, the method is very likely to yield a conditionally stable and convergent solution. Because of this property, the requirement of large computer storage for the multidimensional problem is alleviated. The model is first tested by comparing its simulation with an exact solution for a simplified case. It is then compared favorably with the experimental data. The versatility of the model is demonstrated by applying it to a hypothetical aquifer to derive the direct surface runoff, base runoff, and aquifer storage accumulation following a three-hour storm. (ERA citation 05:031243)