Explicit Computation of Discontinuous Channel Flow
Publication: Journal of Hydraulic Engineering
Volume 112, Issue 6
Abstract
An explicit finite element model for free‐surface flow is developed and shown to be second and fourth‐order accurate with respect to the time and space increments, respectively. The method utilizes a Taylor series expansion for integration in time coupled with the classical Galerkin variational principle. The resulting algebraic equations are linear and can be solved sequentially in the form of smaller uncoupled systems. This results in significantly lower computational and storage requirements while maintaining satisfactory accuracy. Stability limits are established for the method by means of Fourier analysis and the associated phase and amplitude portraits demonstrate a highly selective dissipative character. This makes the method suitable for computation of discontinuous flow, while the explicit nature of the method allows an equally accurate computation of supercritical flow. Following an order of accuracy analysis, the method is extended to two‐space dimensions and several computational examples are presented that show the scheme's performance under various flow conditions. On the basis of these results the method is judged to be more efficient for problems requiring high accuracy near flow discontinuities than, implicit methods with similar properties.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B., Computational Hydraulics, Pitman Publishing, Ltd., London, England, 1979.
2.
Donea, J., “A Taylor‐Galerkin Method for Convective Transport Problems,” Proceedings, 3rd International Conference on Numerical Methods in Laminar and Turbulent Flow, held in Seattle, Wash., Aug., 1983.
3.
Gray, W. G., and Lynch, D. R., “Time‐Stepping Schemes for Finite Element Tidal Model Computations,” Advances in Water Resources, Vol. 1, No. 2, 1977.
4.
Katopodes, N. D., “A Dissipative Galerkin Scheme for Open‐Channel Flow,” ASCE, Journal of Hydraulic Engineering, Vol. 110, Apr., 1984.
5.
Katopodes, N. D., “Two‐Dimensional Surges and Shocks in Open Channels,” ASCE, Journal of Hydraulic Engineering, Vol. 110, June, 1984.
6.
Katopodes, N. D., “Fourier Analysis of Dissipative FEM Channel Flow Model,” ASCE, Journal of Hydraulic Engineering, Vol. 110, July, 1984.
7.
Lohner, R., Morgan, K., and Zienkiewicz, O. C., “The Solution of Nonlinear Hyperbolic Equation Systems by the Finite Element Method,” Institute for Numerical Methods in Engineering, Univ. College of Swansea, England, 1983.
8.
Richtmyer, R. D., and Morton, K. W., Difference Methods for Initial Value Problems, 2nd ed., Interscience Publishers, Wiley, New York, N.Y., 1967.
9.
Wu, C.‐T., “Prediction of Wave Motion in Free Surface Flow,” thesis presented to the Univ. of Michigan, at Ann Arbor, Mich., in 1985, in partial fulfillment of the requirements of the degree of Doctor of Philosophy.
Information & Authors
Information
Published In
Copyright
Copyright © 1986 ASCE.
History
Published online: Jun 1, 1986
Published in print: Jun 1986
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.