An Adaptive-Grid Least Squares Finite Element Solution for Flow in Layered Soils

  • Tsu-Fen Chen
  • Christopher Cox
  • Hasan Merdun
  • Virgil Quisenberry
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3401)


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.


Layer Interface Element Solution Unsaturated Soil Grade Function Discrete Solution 
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  1. 1.
    Richards, L.A.: Capillary Conduction of Liquid through Porous Media. Physics 1(10), 318–333 (1931)CrossRefGoogle Scholar
  2. 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. 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. 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
  5. 5.
    Chen, T.F.: Semidiscrete Least Squares Methods for Linear Convection-Diffusion Problems. Computers Math. Applic. 24(11), 29–44 (1992)zbMATHCrossRefGoogle Scholar
  6. 6.
    Chen, T.F.: Weighted Least Squares Approximations for Nonlinear Hyperbolic Equations. Computers Math. Applic. (to appear)Google Scholar
  7. 7.
    Carey, G.F., Dinh, H.T.: Grading Functions and Mesh Redistribution. Siam J. Numer. Anal. 22, 1028–1040 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chen, T.F., Yang, H.D.: Numerical Construction of Optimal Grids in Two Spatial Dimensions. Computers and Math. with Applications 39, 101–120 (2000)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Tsu-Fen Chen
    • 1
  • Christopher Cox
    • 2
  • Hasan Merdun
    • 3
  • Virgil Quisenberry
    • 4
  1. 1.Department of MathematicsNational Chung Cheng University, MinghsiungChia-YiTaiwan
  2. 2.Department of Mathematical SciencesClemson UniversityClemson
  3. 3.Faculty of Agriculture, Dept. of Agricultural Structure and IrrigationKahramanmaras Sutcu Imam UniversityKahramanmarasTurkey
  4. 4.Department of Crop and Soil Environmental Sciences, 277 Poole Agricultural CenterClemson UniversityClemson

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