An Adaptive-Grid Least Squares Finite Element Solution for Flow in Layered Soils
Groundwater flow in unsaturated soil is governed by Richards equation, a nonlinear convection-diffusion equation. The process is normally convection-dominated, and steep fronts are common in solution profiles. The problem is further complicated if the medium is heterogeneous, for example when there are two or more different soil layers. In this paper, the least squares finite element method is used to solve for flow through 5 layers with differing hydraulic properties. Solution-dependent coefficients are constructed from smooth fits of experimental data. The least squares finite element approach is developed, along with the method for building an optimized, nonuniform grid. Numerical results are presented for the 1D problem. Generalization to higher dimensions is also discussed.
KeywordsLayer Interface Element Solution Unsaturated Soil Grade Function Discrete Solution
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- 2.Romkens, M.J.M., Phillips, R.E., Selim, H.M., Whisler, F.D.: Physical Characteristics of Soils in the Southern Region: Vicksburg, Memphis, and Maury series. South. Coop. Bull. No. 266. MS. Agric. Exp. Stn., Starkville (1985)Google Scholar
- 3.Cline, A.K.: FITPACK - Software Package for Curve and Surface Fitting Employing Splines under Tension. In: Dept. of Comp. Sci., Univ. of Texas, Austin (1981)Google Scholar
- 4.Petzold, L.R.: A Description of DASSL: A Differential/Algebraic System Solver. In: Stepleman, R.S., et al. (eds.) Scientific Computing, Applications of Mathematics and Computing to the Physical Sciences, vol. I. IMACS/North-Holland Publishing Co. (1983)Google Scholar
- 6.Chen, T.F.: Weighted Least Squares Approximations for Nonlinear Hyperbolic Equations. Computers Math. Applic. (to appear)Google Scholar