Conservative Semi-Lagrangian Algorithm for Pollutant Transport in Rivers
Publication: Journal of Environmental Engineering
Volume 125, Issue 5
Abstract
A conservative semi-Lagrangian numerical method for solute transport in steady nonuniform flows is presented. The method is an extension of earlier work on the authors' DISCUS method. Numerical results are compared against an exact solution for solute transport in a nonuniform flow with a linearly varying velocity coefficient and a quadratically varying dispersion coefficient. The method is stable and fully conservative at large Courant and grid Péclet numbers. Accuracy is also good and appears to be primarily related to spatial resolution and grid Péclet number. The method is significantly more computationally efficient than Eulerian numerical methods.
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References
1.
Cerco, C. F., and Cole, T. (1993). “Three dimensional eutrophication model of Chesapeake Bay.”J. Envir. Engrg., ASCE, 119(6), 1006–1025.
2.
Gross, E. S., Koseff, J. R., and Monismith, S. G. (1999). “Evaluation of advective schemes for estuarine salinity simulations.”J. Hydr. Engrg., ASCE, 125(1), 32–46.
3.
Holly, F. M. Jr., and Preissmann, A. P. (1977). “Accurate calculation of transport in two dimensions.”J. Hydr. Div., ASCE, 103(11), 1259–1277.
4.
Leonard, B. P., Lock, A. P., and MacVean, M. K. ( 1995). “The NIRVANA scheme applied to one dimensional advection.” Int. J. Numer. Methods in Fluids, 5, 341–377.
5.
Li, C. W., and Yu, T. S. (1994). “Conservative characteristics-based schemes for mass transport.”J. Hydr. Engrg., ASCE, 120(9), 1089–1099.
6.
Lin, B., and Falconer, R. A. (1997). “Tidal flow and transport modeling using ULTIMATE QUICKEST scheme.”J. Hydr. Engrg., ASCE, 123(4), 303–314.
7.
Manson, J. R., and Wallis, S. G. ( 1995). “An accurate numerical algorithm for advective transport.” Communications in Numer. Methods in Engrg., 11, 1039–1045.
8.
Manson, J. R., and Wallis, S. G. ( 1997). “Towards an accurate fate and transport model for non-uniform surface waters.” Adv. in Envir. Res., 1(1), 98–114.
9.
Roache, P. J. ( 1992). “A flux-based modified method of characteristics.” Int. J. Numer. Methods in Fluids, 15, 1259–1275.
10.
Runkel, R. L., Becala, K. E., Broshears, R. E., and Chapra, S. C. ( 1996). “Reactive solute transport in streams 1. Development of an equilibrium based model.” Water Resour. Res., 32(2), 409–418.
11.
Schnoor, J. ( 1996). Environmental modeling: Fate and transport of pollutants in water, air and soil, Wiley, New York.
12.
Stamou, A. J. ( 1992). “Improving the numerical modeling of river water quality by using high order difference schemes.” Water Res., 26(12), 1563–1570.
13.
Tang, L., and Adams, E. E. ( 1995). “Effect of divergent flow on mass conservation in Eulerian-Lagrangian transport schemes.” Estuarine and Coast. Modeling 1995, Proc., 4th Int. Conf., ASCE, Reston, Va.
14.
Thomman, R. V. (1998). “The future `Golden Age' of predictive models for surface water quality and ecosystem management.”J. Envir. Engrg., ASCE, 124(2), 94–103.
15.
Wallis, S. G., and Manson, J. R. ( 1994). “Numerical simulation of solute transport using the QUICKEST algorithm.” Hydraulic modelling: Development and application of hydraulic models, A. J. Saul, ed., BHR Group, Stratford-upon-Avon, U.K.
16.
Wallis, S. G., and Manson, J. R. ( 1997). “Accurate numerical simulation of advection using large time steps.” Int. J. Numer. Methods in Fluids, 24, 127–139.
17.
Wallis, S. G., Manson, J. R., and Fillippi, L. ( 1998). “A semi-Lagrangian algorithm for one-dimensional advection-diffusion.” Communications in Numer. Methods in Engrg., 14, 671–679.
18.
Walton, R., and Webb, M. (1994). “QUAL2E simulations of pulse loads.”J. Envir. Engrg., ASCE, 120(5), 1017–1031.
19.
Zoppou, C., and Knight, J. H. (1997). “Analytical solutions for Advection and Advection-diffusion equations with spatially variable coefficients.”J. Hydr. Engrg., ASCE, 123(2), 144–148.
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Published In
Journal of Environmental Engineering
Volume 125 • Issue 5 • May 1999
Pages: 486 - 489
History
Published online: May 1, 1999
Published in print: May 1999
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