Small Grid Testing of Finite Difference Transport Schemes
Publication: Journal of Hydraulic Engineering
Volume 114, Issue 3
Abstract
The following finite difference schemes are employed in an alternating direction-implicit format to approximate the linear form of the two-dimensional constituent transport equation: (1) Forward time centered space (FTCS); (2) forward time upwind space (FTUS); (3) spread time centered space (STCS); (4) spread time upwind space (STUS); and (5) flux-corrected transport (FCT). Several test problems for which analytical solutions are available are considered on a small (7 × 8) uniformly spaced computational grid. It is shown that the FCT scheme exhibits superior numerical properties. Additional tests on a (60 × 60) uniformly spaced grid confirm the small grid tests. Although all the small grid tests were performed on a Cray-I supercomputer, it is demonstrated that these tests may be duplicated on currently available mini- and microcomputers. Therefore, the engineer may screen new finite difference transport schemes on local mini- and microcomputers prior to incorporating these schemes in large grid prototype supercomputer simulations.
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References
1.
Boris, J. P., and Book, D. L. (1973). “Flux‐corrected transport I: SHASTA, a fluid transport algorithm that works.” J. of Comp. Phys., II(1), 38–69.
2.
Butler, H. L. (1980). “Evolution of a numerical model for simulating long‐period wave behavior in Ocean‐estuarine systems.” Estuarine and Wetland Processes, P. Hamilton and K. MacDonald, eds., Plenum Press, New York, N.Y.
3.
Gray, W. G., and Pinder, G. F. (1976). “An analysis of the numerical solution of the transport equation.” Water Resour. Res., Jun., 547–555.
4.
Leendertse, J. J. (1970). “A water‐quality simulation model for well‐mixed estuaries and coastal seas.” 1, Principles of Computation, Report RM‐6230‐RC, The Rand Corporation, Santa Monica, Calif.
5.
Leendertse, J. J. (1971). “A water‐quality simulation model for well‐mixed estuaries and coastal seas.” 2, Computation Procedures, R‐708‐NYC, The Rand Corporation, Santa Monica, Calif.
6.
Molenkamp, C. R. (1968). “Accuracy of finite‐difference methods applied to the advection equation.” J. of Appl. Meteorology, 7(Apr.), 160–167.
7.
Peaceman, D. W., and Rachford, H. H. (1955). “The numerical solution of parabolic and elliptic differential equations.” SIAM, 3(1), 28.
8.
Schmalz, R. A. (1981). “Numerical modeling of Mississippi Sound and adjacent areas.” Proc. in Symp. on Mississippi Sound, MASGP‐81‐007, Mississippi‐Alabama Sea Grant Consortium, Jun., Biloxi, Miss. 66–75.
9.
Schmalz, R. A. (1982). “Flux‐corrected transport in an exponentially stretched grid.” Proc. of 1982 Army Num. Analysis and Computers Conf, ARO Report 82‐3, Feb., Vicksburg, Miss., 77–98.
10.
Schmalz, R. A. (1983). “The Development of a Numerical Solution to the Transport Equation: Report 1 Methodology.” Miscellaneous Paper CERC‐83‐2, Coastal Engrg. Res. Center, Vicksburg, Mississippi, Sept.
11.
Schmalz, R. A. (1983). “The development of a numerical solution to the transport equation: report 2 computational procedures.” Miscellaneous Paper CERC‐82‐2, Coastal Engrg. Res. Center, Vicksburg, Miss., Sept.
12.
Schmalz, R. A. (1983). “The development of a numerical solution to the transport equation: report 3 test results.” Miscellaneous Paper CERC‐83‐2, Coastal Engrg. Res. Center, Vicksburg, Miss., Sept.
13.
Schmalz, R. A. (1985). “Numerical model investigation of Mississippi Sound and adjacent areas.” Miscellaneous Paper CERC‐85‐2, Coastal Engrg. Res. Center, Vicksburg, Miss., Feb.
14.
Schmalz, R. A. (1985). “A two‐dimensional vertically integrated, time‐varying estuarine transport model,” Instruction Report EL‐85‐1, U.S. Army Waterways Exp. Station, Vicksburg, Miss., March.
15.
Siemons, J. (1970). “Numerical methods for the solution of diffusion‐advection equations.” Delft Hydraulics Lab., Publ. No. 88, Dec.
16.
Stone, H. L., and Brain, P. L. T. (1963). “Numerical solution of convective transport problems.” A.I.Ch.E.J., Sept., 681–688.
17.
Zalesak, S. T. (1979). “Fully multi‐dimensional flux‐corrected transport algorithms for fluids.” J. of Comp. Phys., 31, 335–362.
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Published In
Journal of Hydraulic Engineering
Volume 114 • Issue 3 • March 1988
Pages: 329 - 336
Copyright
Copyright © 1988 ASCE.
History
Published online: Mar 1, 1988
Published in print: Mar 1988
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