Characteristic Dissipative Galerkin Scheme for Open‐Channel Flow
Publication: Journal of Hydraulic Engineering
Volume 118, Issue 2
Abstract
Many open‐channel flow problems may be modeled as depth‐averaged flows. Petrov‐Galerkin finite element methods, in which up‐wind weighted test functions are used to introduce selective numerical dissipation, have been used successfully for modeling open‐channel flow problems. The underlying consistency and generality of the finite element method is attractive because separate computational algorithms for subcritical and supercritical flow are not required and algorithm extension to the two‐dimensional depth‐averaged flow equations is straightforward. Here, a reconsideration of the fundamental role of the characteristics in the determination of the up‐wind weighting and the use of the conservation form of the governing equations, leads to a new Petrov‐Galerkin scheme entitled the characteristic dissipative Galerkin method. A linear stability analysis illustrates the selective damping of short wavelengths and excellent phase accuracy achieved by this scheme, as well as its insensitivity to parameter variation. Numerical tests are also presented to illustrate the rugged performance of the scheme. This method could be extended to other hyperbolic systems such as: two‐dimensional flows, multilayer fluids, or sediment‐transport problems.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Brooks, A. N., and Hughes, T. J. R. (1982). “Streamline upwind/Petrov‐Galerkin formulations for convection dominated flows with particular emphasis on the in‐compressible Navier‐Stokes equations.” Comput. Methods Appl. Mech. Engrg., 32, 199–259.
2.
Dendy, J. E. (1974), “Two methods of Galerkin‐type achieving optimum rates of convergence for first‐order hyperbolics.” SIAM J. Numer. Anal., 11(3), 637–653.
3.
Fread, D. L. (1988). The NWS DAMBRK model: Theoretical background/user documentation. Nat. Weather Service (NWS), Silver Spring, Md.
4.
Froehlich, D. C. (1985). Discussion of “A dissipative Galerkin scheme for open‐channel flow,” by N. D. Katopodes. J. Hydr. Engrg., ASCE, 111(4), 1200–1204.
5.
Hicks, F. E., and Steffler, P. M. (1990). “Finite element modeling of open channel flow.” Water Resour. Engrg. Report No. 90‐6, Univ. of Alberta, Alberta, Canada.
6.
Hughes, T. J. R., and Mallet, M. (1986). “A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective‐diffusive systems.” Comput. Methods Appl. Mech. Engrg., 58(3), 305–328.
7.
Katopodes, N. D. (1984a). “A dissipative Galerkin scheme for open‐channel flow.” J. Hydr. Engrg., 110(4), 450–466.
8.
Katopodes, N. D. (1984b). “Fourier analysis of dissipative FEM channel flow model.” J. Hydr. Engrg., 110(7), 927–944.
9.
Katopodes, N. D. (1987). “Analysis of transient flow through broken levees.” Turbulence measurements and flow modeling, C. J. Chen, L. D. Chen, and F. M. Holly, Jr., eds., Hemisphere Publishing Corp., Washington, D.C., 301–310.
10.
Raymond, W. H., and Garder, A. (1976). “Selective damping in a Galerkin method for solving wave problems with variable grids.” Monthly Weather Review, 104(12), 1583–1590.
11.
Roache, P. J. (1982). Computational fluid dynamics. Hermosa Publishers, Albuquerque, N.M.
12.
Wang, S. S., and Adeff, S. E. (1987). “A depth integrated model for solving Navier‐Stokes equations using dissipative Galerkin scheme.” Turbulence measurements and flow modeling, C. J. Chen, L. D. Chen, and F. M. Holly, Jr., eds. Hemisphere Publishing Corp., Washington, D.C., 311–321.
13.
Wahlbin, L. B. (1974). “A dissipative Galerkin method for the numerical solution of first order hyperbolic equations.” Mathematical aspects of finite elements in partial differential equations, C. de Boor, ed., Academic Press, New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1992 ASCE.
History
Published online: Feb 1, 1992
Published in print: Feb 1992
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.