Explicit Methods for 2‐D Transient Free Surface Flows
Publication: Journal of Hydraulic Engineering
Volume 116, Issue 8
Abstract
MacCormack and Gabutti explicit finite‐difference schemes are introduced to integrate the equations describing two‐dimensional, unsteady gradually varied flows. Both schemes are second‐order accurate in space and time, allow sharp discontinuous initial conditions, and do not require isolation of the bores. Both sub‐ and supercritical flows may be present simultaneously in different parts of the channel or in a sequence in time. The inclusion of boundaries and stability conditions and the addition of artificial viscosity to smooth high‐frequency oscillations are discussed. To illustrate application of the schemes in hydraulic engineering, two typical problems are solved and the results of different schemes are compared.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B. (1979). Computational hydraulics: Elements of the theory of free‐surface flows. Pitman Publishing Limited, London, United Kingdom.
2.
Abbott, M. B., et al. (1984). “Accuracy of short wave models.” J. Hydr. Engrg., ASCE, 110(10), 1287–1301.
3.
Anderson, D. A., Tannehill, J. D., and Pletcher, R. H. (1984). Computational fluid mechanics and heat transfer. McGraw‐Hill, Inc., New York, N.Y.
4.
Anton, H. (1981). Elementary linear algebra. John Wiley and Sons, Inc., New York, N.Y.
5.
Benque, J. P., Hauguel, A., and Viollet, P. L. (1982). Engineering applications of computational hydraulics. Pitman Advanced Publishing Program, London, United Kingdom.
6.
Chaudhry, M. H. (1987). Applied hydraulic transients. 2nd Ed., Van Nostrand Rein‐hold, New York, N.Y., 379–447.
7.
Chaudhry, M. H. (1991). Open‐channel flow. Prentice‐Hall, Englewood‐Cliffs, N.J.
8.
Cunge, J. A., Holly, F. M., Jr., and Verwey, A. (1980). Practical aspects of computational river hydraulics. Pitman Publishing Limited, London, United Kingdom.
9.
Fennema, R. J. (1985). “Numerical solution of two‐dimensional transient free‐surface flows,” thesis presented to the Washington State University, at Pullman, Wash., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
10.
Fennema, R. J., and Chaudhry, M. H. (1986). “Second‐order numerical schemes for unsteady free‐surface flows with shocks.” Water Resour. Res., 22(13), 1923–1930.
11.
Fennema, R. J., and Chaudry, M. H. (1987). “Simulation of one‐dimensional dam‐break flows.” J. Hydraul. Res., 24(5), 41–51.
12.
Gabutti, B. (1983). “On two upwind finite‐difference schemes for hyperbolic equations in non‐conservative form.” Comput. Fluids, 11(3), 207–230.
13.
Jameson, A., Schmidt, W., and Turkel, E. (1981). “Numerical solutions of the Euler equations by finite volume methods using Runge‐Kutta time‐stepping schemes.” Proc. AIAA 14th Fluid and Plasma Dynamics Conf, American Institute of Aeronautics and Astronautics, 81–1259.
14.
Katopodes, N. D. (1984). “A dissipative Galerkin Scheme for open‐channel flow.” J. Hydr. Engrg., ASCE, 110(6), 450–466.
15.
Katopodes, N. D., and Strcllkoff, T. (1978). “Computing two‐dimensional danibreak flood waves.” J. Hydr. Div., ASCE, 104(9), 1269–1288.
16.
Lax, P. D., and Wendroff, B. (1960). “Systems of conservation laws.” Communications Pure Applied Mathematics, 13, 217–237.
17.
MacCormack, R. W. (1969). “The effect of viscosity in hypervelocity impact cratering.” Paper 69–354, American Institute Aeronautics Astronautics, Cincinnati, Ohio.
18.
Matsutomi, H. (1983). “Numerical computations of two‐dimensional inundation of rapidly varied flows due to breaking of dams.” Proc. XX Congress of the IAHR, International Association for Hydraulics Research, 2, Sept., 479–488.
19.
Moretti, G. (1979). “The λ‐scheme.” Comput. Fluids, 7(3), 191–205.
20.
Sakkas, J. G., and Strelkoff, T. (1973). “Dam‐break flood in a prismatic dry channel.” J. Hydr. Div., ASCE, 99(12), 2195–2216.
21.
Warming, R. F., and Hyett, B. J. (1974). “The modified equation approach to the stability and accuracy analysis of finite‐difference methods.” J. Computational Physics, 14(2), 159–179.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 116 • Issue 8 • August 1990
Pages: 1013 - 1034
Copyright
Copyright © 1990 ASCE.
History
Published online: Aug 1, 1990
Published in print: Aug 1990
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.