Extension of Preissmann Scheme to Two-Dimensional Flows
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 10
Abstract
A numerical solution to the finite difference of two-dimensional (2D) depth-averaged equations on nonstaggered grid points is proposed in this technical note. Following a locally one-dimensional procedure, the basic equations are split into a pair of one-dimensional equations. Therefore, the solution of a 2D problem is reduced to the solution of a sequence of two one-dimensional problems. The discretization of the split one-dimensional equations is obtained with the use of the original Preissmann operator. Using Fourier’s classic linear analysis, stability, dissipation and dispersion with frictional resistance are investigated for the variations of the Courant number and weighting time factor.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abbott, M. B. (1979). Computational hydraulics: Elements of the theory of free surface flows, Pitman Publishing Limited, London.
Abbott, M. B., and Rasmussen, C. H. (1977). “On the numerical modelling of rapid expansions and contractions in models that are two-dimensional in plan.” Proc., 17th Congress IAHR, Vol. 2, Baden-Baden, 229–237.
Fread, D. L. (1974). “Numerical properties of implicit four-point finite difference equations of unsteady flow.” NOAA Technical Memorandum No. NWS HYDRO-18, NOAA.
Hansen, W. (1962). “Hydrodynamical methods applied to oceanographic problems.” Proc., Symp. on Mathematical-Hydrodynamical Methods of Physical Oceanography, Inst. für Meereskunde, Univ. Hamburg, Hamburg, Germany, 25–34.
Hill, J. R. (1981). “Experiments with a nonstaggered, implicit, finite-difference operator for the two-dimensional free surface flow equations.” MS thesis, Texas A&M Univ., College Station, Tex.
Hill, J. R., and Basco, D. R. (1983). “Wiggle instabilities and the 2-D Preissmann scheme.” Frontiers in hydraulic engineering, H. T. Shen, ed., 337–342.
Hirsch, C. (1995). Numerical computation of internal and external flows, Wiley, New York.
Holsters, H. (1962). “Remarque sur la stabilité dans les calculs de marée.” Proc., Symp. on Mathematical-Hydrodynamical Methods of Physical Oceanography, Inst. für Meereskunde, Univ. Hamburg, Hamburg, Germany, 211–225, in French.
Leendertse, J. J. (1967). “Aspects of a computational model for long-period water-wave propagation.” Memorandum No. RM-5294-PR, Rand Corporation, Santa Monica, Calif.
Liggett, J. A. (1975). Stability, Water Resources Publications, M. Yevjevich, ed., Vol. I, Fort Collins, Colo., 259–282.
Preissmann, A. (1961). “Propagation des intumescences dans les canaux et rivières.” Proc., 1st Congress of the French Association for Computation, Grenoble, France, 433–442, in French.
Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, New York.
Vreugdenhil, C. P. (1994). Numerical methods for shallow-water flow, Kluwer, Dordrecht, The Netherlands.
Wesseling, P. (2001). Principles of computational fluid dynamics, Springer, New York.
Yanenko, N. N. (1971). The method of fractional steps, Springer, New York.
Information & Authors
Information
Published In
Copyright
© 2007 ASCE.
History
Received: Dec 30, 2004
Accepted: May 16, 2007
Published online: Oct 1, 2007
Published in print: Oct 2007
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.