Modeling of Flow and Advection Dominant Solute Transport in Variably Saturated Porous Media
Publication: Journal of Hydrologic Engineering
Volume 14, Issue 1
Abstract
In this paper we are presenting a numerical model to simulate transient flow and solute transport through a variably saturated zone. The mixed form of the Richards equation is used for the solution of the flow component as it is mass conserving, and the advection dispersion equation (ADE) is used for the solute transport. The Richards equation is solved numerically by finite difference and modified Picards iteration is used to deal with its inherent nonlinearity, and the resulting matrix is solved by a strongly implicit procedure. The numerical solution of ADE poses oscillations when there is a sharp front due to discontinuity in the solution. In this paper, we are presenting a numerical scheme to address the problems faced by the advective dominant front. The ADE is solved by the operator split method in which advection is solved by explicit finite volume and dispersion by the fully implicit finite difference method. A new numerical scheme is presented for the solution of the advection part of the equation. The advection flux is solved by using a locally one-dimensional approach, with the predictor-corrector method for the time step. Each step is made total variation diminishing to avoid oscillations. Performance of the model is tested for a few cases, like flow and transport into very dry soils, transient unconfined recharge and drainage through seepage face, and transient infiltration into randomly heterogeneous soils. The model is also used to study the effect of water table boundary and seepage face on the movement of solute.
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References
Ababou, R., and Gelhar, L. W. (1988). “A high resolution finite difference simulator for 3D unsaturated flow in heterogeneous media.” Computer Methods in Water Resources, M. Celia, ed., Vol. 1, Elsevier, New York, 175–178.
Antonopoulos, V. Z., and Papazafiriou, Z. G. (1990). “Solutions of one-dimensional water flow and mass transport equations in variably saturated porous media by the finite element method.” J. Hydrol., 119, 151–167.
Bear, J. (1979). Hydraulics of ground water, McGraw-Hill Series in Water Resources and Environmental Engineering, McGraw-Hill, New York.
Celia, M. A., Bouloutas, E. T., and Zarba, R. L. (1990). “A general mass conservative numerical solution for the unsaturated flow equation.” Water Resour. Res., 26(7), 1483–1496.
Clement, T. P., Wise, W. R., and Molz, F. J. (1994). “A physically based two dimensional finite difference algorithm for modeling variably saturated flow.” J. Hydrol., 161, 71–90.
Cooley, R. L. (1983). “Some new procedures for numerical solution of variably saturated flow problems.” Water Resour. Res., 19(5), 1271–1285.
Cox, R. A., and Nishikawa, T. (1991). “A new total variation diminishing scheme for the solution of advective-dominant solute transport.” Water Resour. Res., 27(10), 2645–2654.
Farthing, M. W., and Miller, C. T. (2001). “A comparison of high resolution, finite volume, adaptive-stencil schemes for simulating advective-dispersive transport.” Adv. Water Resour., 24, 29–48.
Freeze, R. A. (1971a). “Influence of the unsaturated flow domain on seepage through earth dams.” Water Resour. Res., 7(4), 929–941.
Freeze, R. A. (1971b). “Three-dimensional transient saturated-unsaturated flow in a ground water basin.” Water Resour. Res., 7, 347–366.
Freeze, R. A., and Cherry, J. A. (1979). Groundwater, Prentice-Hall, Englewood Cliffs, N.J.
Godunov, S. (1959). “A finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics.” Mat. Sb., 47, 428–441.
Harten, A. (1983). “High resolution schemes for hyperbolic conservation laws.” J. Comput. Phys., 49, 357–393.
Haverkamp, R., Vauclin, M., Touma, J., Wieranga, P. J., and Vachaud, G. (1977). “Comparison of numerical simulation models for one dimensional infiltration.” Soil Sci. Soc. Am. J., 41, 285–294.
Jyothish, S. (1999). “A hybrid finite volume model for reactive solute transport in ground water.” Ph.D. thesis, Indian Institute of Science, Bangalore, India.
Khaleel, R., Yeh, T. C. J., and Lu, Z. (2002). “Upscaled flow and transport properties for heterogeneous unsaturated media.” Water Resour. Res., 38(5), 11.1–11.12.
Kirkland, M. R., Hills, R. G., and Wierenga, P. J. (1992). “Algorithms for solving Richards’ equation for variably saturated soils.” Water Resour. Res., 28(8), 2049–2058.
Le Veque, R. J. (2002). Finite volume methods for hyperbolic problems, Cambridge University Press, Cambridge, U.K.
Li, C. W. (1996). “Modelling variably saturated flow and solute transport into sandy soil.” J. Hydrol., 186, 315–325.
Milly, P. C. D. (1985). “A mass conservative procedure for time stepping in models of unsaturated flow.” Adv. Water Resour., 8, 32–36.
Mohan Kumar, M. S., Sridharan, K., and Lakshmana Rao, N. S. (1987). “Modified strongly implicit procedure for groundwater flow analysis.” J. Hydrol., 87, 299–314.
Mualem, Y. (1976). “A new model for predicting the hydraulic conductivity of porous media.” Water Resour. Res., 12(3), 513–552.
Putti, M., Yeh, W. W.-G., and Mulder, W. A. (1990). “A triangular finite volume approach with high resolution upwind terms for the solution of ground water transport equations.” Water Resour. Res., 26(12), 2865–2880.
Roe, P. L. (1986). “Approximate Reimann solvers, parameter vectors and difference schemes.” J. Comput. Phys., 43, 357–372.
Soraganvi, V. S. (2005). “Numerical and stochastic modelling of flow and transport in the Vadose zone.” Ph.D. thesis, Indian Institute of Science, Bangalore, India.
Soraganvi, V. S., Ababou, R., and Mohan Kumar, M. S. (2006). “Stochastic modeling of unsaturated flow and transport: Numerical experiments, macroscopic behaviour and upscaling.” Proc., Int. Conf. IAHR-GW 2006 Groundwater in Complex Environments, Toulouse, France.
Stone, H. L. (1968). “Iterative solution of implicit approximations of multidimensional partial differential equations.” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 5, 530–558.
Sun, N.-Z., and Yeh, W. W.-G. (1983). “A proposed upstream weight numerical method for simulating pollutant transport in groundwater.” Water Resour. Res., 19(6), 1489–1500.
Sweby, P. K. (1985). “High resolution TVD schemes using flux limiters.” Lect. Appl. Math., 22, 289–309.
Tompson, A. F. B., Ababou, R., and Gelhar, L. W. (1989). “Implementation of the three dimensional turning band random field generator.” Water Resour. Res., 25(10), 2227–2243.
van Albada, G. D., van Leer, B., and Roberts, W. W. (1982). “A comparative study of computational methods in cosmic gas dynamics.” Astron. Astrophys., 108, 76–86.
van Genuchten, M. Th. (1980). “A closed form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44, 892–898.
van Leer, B. (1977). “Towards the ultimate conservative finite difference scheme, IV A new approach to numerical convection.” J. Comput. Phys., 23, 263–275.
Vauclin, M., Khanji, D., and Vachaud, G. (1975). “Two dimensional numerical analysis of transient water transfer in saturated-unsaturated soils.” Modeling and simulation of water resource systems, G. C. Vansteenkiste, ed., North-Holland, Amsterdam, The Netherlands, 299–323.
Vauclin, M., Khanji, D., and Vachaud, G. (1979). “Experimental and numerical study of a transient two dimensional unsaturated-saturated water table recharge problem.” Water Resour. Res., 15(5), 1089–1101.
Yu, T. S., and Li, C. W. (1994). “Efficient higher order backward characteristics schemes for transient advection.” Int. J. Numer. Methods Fluids, 19(11), 997–1012.
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Information
Published In
Journal of Hydrologic Engineering
Volume 14 • Issue 1 • January 2009
Pages: 1 - 14
Copyright
© 2009 ASCE.
History
Received: Dec 15, 2006
Accepted: Apr 10, 2008
Published online: Jan 1, 2009
Published in print: Jan 2009
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