Finite Analytic Model for Flow and Transport in Unsaturated Zone
Publication: Journal of Engineering Mechanics
Volume 126, Issue 5
Abstract
The finite analytic method is employed to solve the vertical, two-dimensional subsurface flow and transport equations in an unsaturated zone. The finite analytic method treats the nonlinear coefficient terms of the governing equations as constants in the element so that linearized partial differential equations can be obtained and solved in each element. The accuracy and limitations of the numerical method are systematically explored. The flow and transport simulations are examined using a one-dimensional laboratory infiltration test and an analytical solution of a two-dimensional subsurface transport problem, respectively. In the advection-dominant, vertical, one-dimensional infiltration problem, nine spatial weighting schemes are proposed to evaluate the averaged unsaturated hydraulic conductivity in a discretized element. Among them, the geometric mean weighting scheme provides the most accurate results as compared with the infiltration data. In verification of the two-dimensional solute transport problem, the nine-node elements are placed in the interior domain, and different layers of five-node elements are placed at the boundaries to investigate if the numerical experiment setup was proper and the algorithm was accurate. The developed numerical model is then applied to an irregular-domain landfill leaching problem to reveal the features of subsurface transport in unsaturated zone. Numerical aspects to be further explored are suggested.
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References
1.
Anderson, M. P. (1979). “Using models to simulate the movement of contaminants through groundwater systems.” Critical Rev. in Envir. Control, 9(2), 97–156.
2.
Bear, J. (1979). Hydraulics of groundwater water. McGraw-Hill, New York, 213–234.
3.
Carslaw, H. S., and Jaeger, J. C. (1971). Conduction of heat in solids. Oxford University Press, London.
4.
Carlson, K. D. ( 1993). “Finite analytic numerical simulation of twodimensional flow problems with irregular boundaries in Cartesian coordinates,” MS thesis, Dept. of Mech. Engrg., University of Iowa, Iowa City, Iowa.
5.
Chen, C. J. ( 1989). “Finite analytic numerical method.” Handbook of numerical heat transfer, Wiley, New York.
6.
Chen, C. J., and Chen, H. C. (1984a). “Development of finite analytic numerical method for unsteady two-dimensional Navier-Stokes equation.” J. Comp. Physics, 53(2), 209–226.
7.
Chen, H. C., and Chen, C. J. (1984b). “Development of finite analytic numerical method for unsteady three-dimensional Navier-Stokes equations: computation of internal flows.” ASME FED, 14, 159–165.
8.
Haverkamp, R., and Vauclin, M. (1979). “A note on estimating finite difference interblock hydraulic conductivity values for transient unsaturated flow problems.” Water Resour. Res., 15(1), 1354–1360.
9.
Hwang, J. C., Chen, C. J., Sheikhoslami, M., and Panigrahi, B. K. (1985). “Finite analytic numerical solution for two-dimensional groundwater solute transport.” Water Resour. Res., 21(90), 1354–1360.
10.
Leonard, B. P., and Mokhtari, S. (1990). “Beyond first-order upwinding: the ultra-sharp alternative for non-oscillatory steady-state simulation of convection.” Int. J. Numer. Methods in Engrg., 30, 729–766.
11.
Li, W., Xie, Q., and Chen, C. J. (1989). “Finite analytic solution of flow over spillways.”J. Engrg. Mech., ASCE, 115(12), 2635–2647.
12.
Pi, Z., and Hjelmfelt Jr., A. T. (1994). “Hybrid finite analytic solution of lateral subsurface flow.” Water Resour. Res., 30(5), 1471–1478.
13.
Tien, H. C. ( 1992). “Finite analytic method for computational domain with irregular boundaries,” PhD thesis, Dept. of Appl. Math., University of Iowa, Iowa City, Iowa.
14.
Touma, J., and Vauclin, M. (1986). “Experimental and numerical analysis of two phase infiltration in a partially saturated soil.” Transport in Porous Media, 1, 28–55.
15.
Tsai, W. F., Chen, C. J., and Tien, H. C. (1993). “Finite analytic numerical solutions for unsaturated flow with irregular boundaries.”J. Hydr. Engrg., ASCE, 119(11), 1274–1298.
16.
Warrick, A. W., and Lomen, D. O. (1976). “Time-dependent linearized infiltration. III: Strip and disc sources.” Soil Sci. Soc. Am. J., 40, 639–643.
17.
Yeh, G. T. (1987). “FEMWATER: a finite-element model of water flow through saturated-unsaturated porous media.” Rep. ORNL-5567/R1, Oak Ridge National Laboratory, Oak Ridge, Tenn.
18.
Yeh, G. T., and Ward, D. S. (1980). “FEMWATER: a finite-element model of water flow through saturated-unsaturated porous media.” Rep. ORNL-5567, Oak Ridge National Laboratory, Oak Ridge, Tenn.
19.
Zeng, X. J., and Li, W. ( 1987). “The stability and convergence of finite analytic method for unsteady two-dimensional convective transport equations.” Turbulence measurements and flow modeling, C. J. Chen, L. D. Chen, and F. M. Holly, eds., Hemisphere Publishing, Bristol, Pa., 427–433.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 126 • Issue 5 • May 2000
Pages: 470 - 479
History
Received: Mar 8, 1999
Published online: May 1, 2000
Published in print: May 2000
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