Finite Element Characteristic Advection Model
Publication: Journal of Hydraulic Engineering
Volume 114, Issue 9
Abstract
For advection‐dominated transport processes, the traditional numerical techniques for solving the advection‐diffusion equation fail because of numerical oscillations. Fractional step solutions, in which the advection and diffusion processes are treated in separate steps, have been proposed as one way of overcoming this problem. Here a solution to the advection step based on the method of characteristics on a fixed grid is used. Interpolation is achieved with the finite element technique. Linear and quadratic elements are evaluated in terms of artificial diffusion, phase, and other errors. It was found that linear interpolation creates too much numerical diffusion, while the quadratic scheme is reasonably accurate, but under certain conditions generates spurious extrema. A method retaining the accuracy of the quadratic interpolation and eliminating its shortcoming is suggested. Boundary conditions and source loadings are considered in detail. An application of the model to salinity distribution resulting from canal discharges in Biscayne Bay is described.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baptista, A. E. de M., Adams, E. E., and Stolzenbach, K. D. (1984). “Eulerian‐Lagrangian analysis of pollutant transport in shallow water.” R296, Ralph M. Parsons Lab., Dept. of Civil Engineering, MIT, Cambridge, Mass.
2.
Benque, J. P., et al. (1982). “New method for tidal current computation.” J. Wtwy., Port, Coast., Oc. Div., ASCE, 108(WW3), 396–417.
3.
Chapra, S. C., and Canale, R. P. (1985). Numerical methods for engineers. McGraw‐Hill Publishing Co., New York, N.Y., 570.
4.
Chin Fatt, J., and Wang, J. D. (1986). “Canal impact on Biscayne Bay salinities.” Tech. Report No. 86‐005, Rosenstiel School of Marine and Atmospheric Science, Miami, Fla., 229.
5.
Christodoulou, G. C., and Connor, J. J. (1980). “Dispersion in two‐layer stratified water bodies.” J. Hydr. Div., ASCE, 106(HY4), 557–573.
6.
Fischer, H. B., et al. (1979). Mixing in inland and coastal water. Academic Press, New York, N.Y., 483.
7.
Hasbani, Y., Lione, E., and Bercovier, M. (1983). “Finite elements and characteristics applied to advection‐diffusion equations.” Comput. Fluids, 11(2), 71–83.
8.
Heinrich, J. C., Huyakorn, P. S., and Zienkiewice, D. C. (1977). “An ‘upwind’ finite element scheme for two‐dimensional convective transport equation.” Int. J. Numer. Methods Eng., 11(1), 131–143.
9.
Holly, F. M., Jr., and Preissman, A. (1977). “Accurate calculation of transport in two dimensions.” J. Hydr. Div., ASCE, 103(HY11), 1259–1277.
10.
Holly, F. M., Jr., and Usseglio‐Polatera, J.‐M. (1986). “Dispersion simulation in two‐dimensional tidal flow.” J. Hydr. Engrg., ASCE, 112(7), 905–926.
11.
Roache, P. J. (1976). Computational fluid dynamics. Hermosa Publishers, Albuquerque, N.M., 446.
12.
Wang, J. D. (1978). “Real‐time flow in unstratified shallow water.” J. Wtrwy., Port, Coast., Oc. Div., ASCE, 104(WW1), 53–68.
13.
Zalesak, S. T. (1979). “Fully multidimensional flux‐corrected transport algorithms for fluids.” J. of Comp. Physics, 31(3), 335–362.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 114 • Issue 9 • September 1988
Pages: 1098 - 1114
Copyright
Copyright © 1988 ASCE.
History
Published online: Sep 1, 1988
Published in print: Sep 1988
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.