Unsteady Finite-Analytic Method for Solute Transport in Ground-Water Flow
Publication: Journal of Engineering Mechanics
Volume 121, Issue 2
Abstract
This work illustrates the development and application of the unsteady finite-analytic (FA) numerical solution for the migration of ground-water contamination. A functional/optimal time-weighting factor, established based on the analytic solutions of the one-dimensional, linear advection-diffusion equation, is proposed for the expression of the unsteady term in the solute-transport equation. The upstream shift nature of FA coefficients and the all-positive algebraic equation automatically originate from the FA solution, providing a physically meaningful and stable numerical scheme. Another feature of the method presented is that a very large time interval can be used in the numerical simulation. Therefore, only few time steps are needed to complete the whole computation. In the examples, the performance of unsteady FA numerical solutions is demonstrated by simulating the solute transport emitting from a Gaussian-line source. It is shown that the use of the functional time-weighting factor associated with the finite-analytic method appears to be a better choice for avoiding numerical diffusions and oscillations than, through comparison with, the fully implicit (time-weighting factor = 0) and the Crank-Nicholson (time-weighting factor = 0.5) FA schemes.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bravo, R. H. (1991). “Development of the three-dimensional finite analytic method for simulation of fluid flow and conjugate heat transfer,” PhD thesis, Univ. of Iowa, Iowa City, Iowa.
2.
Chen, H. C., and Chen, C. J. (1982). The finite analytic method: Vol. 4 . Inst. of Hydr. Res., Univ. of Iowa, Iowa City, Iowa.
3.
Chen, C. J., and Chen, H. C.(1984a). “Development of finite analytic numerical method for unsteady two-dimensional Navier-Stokes equation.”J. Computational Phys., 53(2), 209–226.
4.
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 24, Am. Soc. Mech. Engrs. (ASME), New York, N.Y., 159–165.
5.
Chen, C. K., and Chen, T. M.(1987). “Hybrid Laplace transform/finite element method for one-dimensional transient heat conduction problems.”Comp. Methods Appl. Mech. Engrg., 63(1), 83–95.
6.
Chen, H. T., and Chen, C. K.(1988). “Application of hybrid Laplace transform/finite difference method to transient heat conduction problems.”Numerical Heat Transfer, 14(1), 343–356.
7.
Chen, C. K., and Chen, T. M.(1991). “New hybrid Laplace transform/finite element method for three-dimensional transient heat conduction problem.”Int. J. for Numerical Methods in Engrg., 32, 45–61.
8.
Gureghian, A. B., Ward, D. S., and Cleary, R. W.(1980). “A finite element model for the migration of leachate from a sanitary landfill in Long Island, New York. Part I: Theory.”Water Resour. Bull., (Oct.), 16(5), 900–906.
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(9), 1354–1360.
10.
Lee, S. L.(1988). “A new numerical formulation for parabolic differential equation under the consideration of large time step.”Int. J. for Numerical Methods in Engrg., 26(7), 1541–1549.
11.
Li, S. G.(1988). “Optimal exponential difference scheme for solving parabolic equations.”Numerical Heat Transfer, 14(3), 357–376.
12.
Li, S. G., Ruan, F., and McLaughlin, D.(1992). “A space-time accurate method for solving solute transport problems.”Water Resour. Res., 28(9), 2297–2306.
13.
Liggett, J. A., and Liu, P. L.-F. (1983). “The boundary integral equation method for porous media flow.”The boundary integral, George Allen and Unwin Ltd.
14.
Sudicky, E. A.(1989). “The Laplace transform Galerkin technique: a time-continuous finite element theory and application to mass transport in groundwater.”Water Resour. Res., 25(18), 1833–1846.
15.
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 Corp., New York, N.Y., 427–433.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Feb 1, 1995
Published in print: Feb 1995
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.