Evaluation of Advective Schemes for Estuarine Salinity Simulations
Publication: Journal of Hydraulic Engineering
Volume 125, Issue 1
Abstract
Several advective transport schemes are considered in the context of two-dimensional scalar transport. To review the properties of these transport schemes, results are presented for simple advective test cases. Wide variation in accuracy and computational cost is found. The schemes are then applied to simulate salinity fields in South San Francisco Bay using a depth-averaged approach. Our evaluation of the schemes in the salinity simulation leads to some different conclusions than those for the simple test cases. First, testing of a stable, but nonconservative Eulerian-Lagrangian scheme does not produce accurate results, showing the importance of mass conservation. Second, the conservative schemes that are stable in the simulation reproduce salinity data accurately independent of the order of accuracy of each scheme. Third, the leapfrog-central scheme was stable for the model problems but not stable in the unsteady, free surface computations. Thus, for the simulation of salinity in a strongly dispersive setting, the most important properties of a scalar advection scheme are stability and mass conservation.
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References
1.
Blumberg, A. F., and Mellor, G. L. ( 1987). “A description of a three-dimensional coastal ocean circulation model.” Three dimensional coastal ocean models, N. S. Heaps, ed., Vol. 118, American Geophysical Union, Washington, D.C., 1–16.
2.
Burau, J. R., Monismith, S. G., and Koseff, J. R. ( 1993). “Comparison of advective transport algorithms with an application in Suisun Bay, a sub-embayment of San Francisco Bay, California.” Proc., 1993 Hydr. Engrg. Conf., ASCE, New York, 1628–1634.
3.
Casulli, V. ( 1990). “Semi-implicit finite difference methods for the two-dimensional shallow water equations.” J. Comput. Phys., 86, 56–74.
4.
Casulli, V., and Cattani, E. ( 1994). “Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow.” Comp. and Mathematics with Applications, 27(4), 99–112.
5.
Casulli, V., and Cheng, R. T. ( 1992). “Semi-implicit finite difference methods for three-dimensional shallow water flow.” Int. J. Numer. Methods Fluids, 15, 629–648.
6.
Cheng, R. T., and Casulli, V. ( 1984). “On Lagrangian currents with applications in South San Francisco Bay, California.” Water Resour. Res., 18(6), 1652–1662.
7.
Cheng, R. T., and Casulli, V. ( 1992). “Dispersion in tidally-averaged transport equation.” Dynamics and exchanges in estuaries and the coastal zone, D. Prandle, ed., Vol. 40, American Geophysical Union, Washington, D.C., 409–428.
8.
Cheng, R. T., Casulli, V., and Gartner, J. W. ( 1993). “Tidal, residual, intertidal mudflat (TRIM) model and its applications to San Francisco Bay, California.” Estuar., Coast. Shelf Sci., 369, 235–280.
9.
Conomos, T. J., Smith, R. E., and Gartner, J. W. ( 1993). “Environmental setting of San Francisco Bay.” Hydrobiologia, J. E. Cloern and F. H. Nichols, eds., Vol. 129, Dr. W. Junk Publishers, Dordrecht, The Netherlands, 1–12.
10.
Edmunds, J. L., Cole, B. E., Cloern, J. E., and Dufford, R. G. ( 1997). “Studies of the San Francisco Bay, California, estuarine ecosystem: Pilot regional monitoring results, 1995.” Open-File Rep. 97-15, U.S. Geological Survey, Menlo Park, Calif.
11.
Gomez-Reyes, E., and Blumberg, A. F. ( 1995). “Pollutant transport in coastal water bodies.” Proc., 2nd Int. Conf. on Comp. Modelling of Seas and Coast. Regions, Computational Mechanics Publications, Southampton, Boston, 87–94.
12.
Greenspan, D., and Casulli, V. ( 1988). Numerical analysis for applied mathematics, science, and engineering, 1st Ed., Addison-Wesley, Reading, Mass.
13.
Gross, E. S. ( 1998). “Numerical modeling of hydrodynamics and scalar transport in an estuary,” PhD thesis, Stanford University, Stanford, Calif.
14.
Hecht, M. W., Holland, W. R., and Rasch, P. J. ( 1995). “Upwind-weighted advection schemes for ocean tracer transport: An evaluation in a passive tracer context.” J. Geophys. Res., 100, 20,763–20,778.
15.
Hirsch, C. ( 1988). Numerical computation of internal and external flows, Volume 1: Fundamentals of numerical discretization, 1st Ed., Wiley, Chichester, England.
16.
Hirsch, C. ( 1990). Numerical computation of internal and external flows, Volume 2: Computational methods for inviscid and viscous flows, 1st Ed., Wiley, Chichester, England.
17.
James, I. D. ( 1996). “Advection schemes for shelf sea models.” J. Marine Sys., 8, 237–254.
18.
Johnson, B. H., Kim, K. W., Heath, R. E., Hsieh, B. B., and Butler, H. L. (1993). “Validation of a three-dimensional hydrodynamic model of Chesapeake Bay.”J. Hydr. Engrg., ASCE, 119, 2–20.
19.
Leonard, B. P. ( 1979). “A stable and accurate convective modeling procedure based on quadratic upstream interpolation.” Comput. Methods Appl. Mech. Engrg., 19, 59–98.
20.
Leonard, B. P. ( 1991). “The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection.” Comp. Methods Appl. Mech. Engrg., 88, 17–74.
21.
Leonard, B. P., Lock, A. P., and MacVean, M. K. ( 1996). “Conservative explicit unrestricted-time-step multidimensional constancy-preserving advection schemes.” Monthly Weather Rev., 124, 2588–2606.
22.
LeVeque, R. J. ( 1992). Numerical methods for conservation laws, 2nd Ed., Birkhäuser, Basel, Germany.
23.
Lin, B., and Falconer, R. A. (1997). “Tidal flow and transport modeling using ULTIMATE QUICKEST scheme.”J. Hydr. Engrg., ASCE, 123, 303–314.
24.
Lin, S., and Rood, R. B. ( 1996). “Multidimensional flux-form semi-Lagrangian transport schemes.” Monthly Weather Rev., 119, 2046–2070.
25.
Roe, P. L. ( 1985). “Some contributions to the modelling of discontinuous flows.” Lect. in Appl. Mathematics, 22, 163–193.
26.
Selleck, R. E., Pearson, E. A., Glenne, Bard, and Storrs, P. N. ( 1966). “Physical and hydrological characteristics of San Francisco Bay.” Rep. 65-10, Sanitary Engrg. Res. Lab., University of California at Berkeley, Berkeley, Calif.
27.
Signell, R. P., and Butman, P. ( 1992). “Modeling tidal exchange and dispersion in Boston Harbor.” J. Geophys. Res., 97, 591–606.
28.
Smolarkiewicz, P. K. ( 1984). “A fully multidimensional positive-definite advection transport algorithm with small implicit diffusion.” J. Comput. Phys., 54, 325–362.
29.
Smolarkiewicz, P. K., and Grabowski, W. W. ( 1990). “The multidimensional positive definite advection transport algorithm: Nonoscillatory option.” J. Comput. Phys., 86, 355–375.
30.
van Eijkeren, J. C. H. ( 1993). “Backward semi-Lagrangian methods: An adjoint equation method.” Numerical methods for advection-diffusion problems, C. B. Vreugdenhil and B. Koren, eds., Vol. 45, Notes on numerical fluid mechanics, Chapter 9, Vieweg, Washington, D.C., 215–241.
31.
van Eijkeren, J. C. H., de Haan, B. J., Stelling, G. S., and van Stijn, T. L. ( 1993). “Linear upwind biased methods.” Numerical methods for advection-diffusion problems, C. B. Vreugdenhil and B. Koren, eds., Vol. 45, Notes on numerical fluid mechanics, Chapter 3, Vieweg, Washington, D.C., 55–91.
32.
Walters, R. A. ( 1982). “Low-frequency variations in sea level and currents in South San Francisco Bay.” J. Phys. Oceanography, 12, 658– 668.
33.
Walters, R. A., Cheng, R. T., and Conomos, T. J. ( 1985). “Time scales of circulation and mixing processes of San Francisco Bay waters.” Hydrobiologia, Dordrecht, The Netherlands, 129, 13–36.
34.
Zimmerman, J. T. F. ( 1986). “The tidal whirlpool: A review of horizontal dispersion by tidal and residual currents.” Netherlands J. Sea Res., The Netherlands, 20, 133–154.
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Received: Mar 1, 1996
Published online: Jan 1, 1999
Published in print: Jan 1999
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