An Eigenvalue Technique for Solute Transport
Publication: Journal of Hydraulic Engineering
Volume 110, Issue 10
Abstract
The spatially discretized linear equation of groundwater solute transport in a steady flow field was solved by an eigenvalue technique. The methods employed to impose the commonly encountered boundary conditions in the formulation and solution procedures are described in detail. Using the eigenvalue technique the dynamic system equation is decoupled and the time integration can be done independently and continuously for each nodal point. Finally, an explicit expression is obtained for each nodal point as a function of time. This method can provide convenience of data retrieval, particularly in ground‐water management modeling.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bellman, R. E., Introduction to Matrix Analysis, McGraw‐Hill Book Co., Inc., New York, N.Y., 1960.
2.
Chen, C. T., Introduction to Linear System Theory, Holt, Rinehart and Winston, Inc., New York, N.Y., 1970.
3.
Desai, C. S., Elementary Finite Element Method, Prentice Hall, New York, N.Y., 1979.
4.
Faust, C. R., and Mercer, J. W., “Groundwater Modeling: Recent Developments,” Groundwater, Vol. 18, No. 6, 1980, pp. 569–577.
5.
Freeze, R. A., and Cherry, J. A., Groundwater, Prentice Hall, New York, N.Y., 1979.
6.
Gureghian, A. B., Ward, D. S., and Cleary, R. W., “A Finite‐Element Model for the Migration of Leachate from a Sanitary Landfill in Long Island, New York,” Water Resour. Bulletin, Vol. 16, No. 5, 1980, pp. 900–906.
7.
Guymon, G. L., “A finite Element Solution of the One‐Dimensional Diffusion‐Convection Equation,” Water Resour. Res., Vol. 6, No. 1, 1970, pp. 204–210.
8.
Huyakorn, P. S., and Nilkuha, K., “Solution of Transient Transport Equation Using Upstream Finite Element Scheme,” Appl. Math. Model., IPC Business Press, Vol. 3, No. 1, 1979, pp. 7–17.
9.
Hwang, J. C., and Koerner, R. M., “Groundwater Pollution Source Identification from Limited Monitoring Well Data: Part I—Theory and Feasibility,” Journal of Hazardous Material, 1983.
10.
Hwang, J. C., and Koerner, R. M., “Determination of Location and Number of Groundwater Monitoring Wells,” presented at the ASCE Spring Convention, held at Philadelphia, Pa. 1983.
11.
Kagstrom, B., and Ruhe, A., “Algorithm 560 JNF, An Algorithm for Numerical Computation of the Jordan Normal of a Complex Matrix,” ACM Transaction on Math. Software, Vol. 6, No. 3, 1980, pp. 437–443.
12.
Kuiper, L. K., “Analytical Solution of Spatially Discretized Groundwater Flow Equations,” Water Resour. Res., Vol. 9, No. 4, 1973, pp. 1094–1097.
13.
Pinder, G. F., and Frind, E. O., “Application of Galerkin's Procedure to Aquifer Analysis,” Water Resour. Res., Vol. 8, No. 1, 1972, pp. 108–120.
14.
Sahuquillo, A., “An Eigenvalue Numerical Technique for Solving Unsteady Linear Groundwater Models Continuously in Time,” Water Resour. Res., Vol. 19, No. 1, 1983, pp. 87–93.
15.
Scheidegger, A. E., “General Theory of Dispersion in Porous Media,” J. Geophys. Res., Vol. 66, No. 10, 1961, pp. 3273–3278.
16.
Smith, B. T., et al., “Matrix Eigensystems Routines—EISPACK Guide,” 2nd ed., Springer‐Verlag, 1976.
17.
Willis, R., “A Planning Model for the Management of Groundwater Quality,” Water Resour. Res., Vol. 15, No. 6, 1979, pp. 1305–1312.
18.
Yeh, G. T., and Ward, D. A., “FEMWASTE, A Finite‐Element Model of Waste Transport through Saturated‐Unsaturated Porous Media,” Oak Ridge National Lab., Report No. 5601, 1981.
Information & Authors
Information
Published In
Copyright
Copyright © 1984 ASCE.
History
Published online: Oct 1, 1984
Published in print: Oct 1984
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.