Three-dimensional analytical solutions of Richards' equation for a box-shaped soil sample with piecewise-constant head boundary conditions on the top

Journal of Hydrology

Volumn 336, Issue 3-4, 2007, Pages 391-400

  Tracy, F T ^a  

^a US ARMY ENGINEER RESEARCH AND DEVELOPMENT CENTER   (United States)

Author keywords

Analytical solutions; Groundwater modeling; Richards' equation; Unsaturated flow; Vadose zone

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

GROUNDWATER MODELING; RICHARDS' EQUATION; UNSATURATED FLOW; VADOSE ZONE;

GROUNDWATER FLOW;

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; GROUNDWATER FLOW; HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

ANALYTICAL METHOD; FLOW MODELING; GROUNDWATER FLOW; HYDRAULIC CONDUCTIVITY; MODEL TEST; NUMERICAL MODEL; RICHARDS EQUATION; STEADY-STATE EQUILIBRIUM; THREE-DIMENSIONAL FLOW; UNSATURATED FLOW; VADOSE ZONE;

EID: 33947176062     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2007.01.011     Document Type: Article

References (17)

1. Broadridge P., and White I. Constant rate infiltration: a versitle nonlinear model, 1. Analytic solution. Water Resour. Res. 8 4 (1973) 975-986
2. Chen J.M., Tan Y.C., Chen C.H., and Parlange J.Y. Analytical solutions for linearized Richards equation with arbitrary time-dependent surface fluxes. Water Resour. Res. 37 4 (2001) 1091-1093
3. Duffy D.G. Transform Methods for Solving Partial Differential Equations (1994), CRC Press, Ann Arbor, Michigan
4. Elnawawy O.A., and Azmy Y.Y. Cell analytical-numerical method for solution of the Richards equation. Finite Elements Water Resour. 1 (1992) 203-209
5. Fityus S.G., and Smith D.W. Solution of the unsaturated soil moisture equation using repeated transforms. Int. J. Numer. Anal. Methods Geomech. 25 15 (2001) 1501-1524
6. Gardner W.R. Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci. 85 4 (1958) 228-232
7. Hogarth W.L., and Parlange J.Y. Application and improvement of a recent approximate analytical solution of Richards' equation. Water Resour. Res. 36 7 (2000) 1965-1968
8. Irmay S. On the hydraulic conductivity of unsaturated soils. Econ. Transit., AGU 35 (1954)
9. Marinelli F., and Durnford D.S. Semianalytical solution to Richards' equation for layered porous media. J. Irrig. Drain. Eng. 124 6 (1998) 290-299
10. Seǵol G. Classic Groundwater Simulations (1994), Prentice Hall, Englewood Cliffs, New Jersey pp. 316-323
11. Seǵol G. Classic Groundwater Simulations (1994), Prentice Hall, Englewood Cliffs, New Jersey p. 352
12. Tracy F.T. 1-D, 2-D, and 3-D analytical solutions of unsaturated flow in groundwater. J. Hydrol. 170 (1995) 199-214
13. Tracy F.T. Evaluation of the non-isothermal/thermal unsaturated/saturated flow and transport (NUFT) code using analytical solutions. IAHR (1997) 427-432
14. Tracy F.T. Clean two- and three-dimensional analytical solutions of Richards equation for testing numerical solvers. Warer Resour. Res. 42 (2006) W08503
15. van Genuchten M. A closed-form equation for producing the hydraulic conductivity of unsaturated soils. Soil Sci. Am. J. 44 (1980) 892-898
16. Warrick A.W. Soil Water Dynamics (2003), Oxford University Press, New York pp. 247-258
17. Wu Y., and Pan L. An analytical solution for transient radial flow through unsaturated fractured porous media. Water Resour. Res. 41 2 (2005) 1-6