Depth-Averaged Simulation of Supercritical Flow in Channel with Wavy Sidewall
Publication: Journal of Hydraulic Engineering
Volume 126, Issue 6
Abstract
Supercritical flow in a channel with a wavy sidewall is numerically simulated by solving the two-dimensional (2D) depth-averaged equations using two different second-order accurate finite-difference schemes: ADI and MAC. ADI is an implicit model that uses an alternating-direction-implicit (ADI) scheme to solve the governing equations. MAC is an explicit model employing the MacCormack two-step predictor-corrector scheme. To accurately simulate the wavy sidewall, both models solve the governing equations in transformed computational coordinates. Bottom friction is computed using the Manning formula and the effective stresses are modeled with a constant eddy-viscosity turbulence model. As is customary, the stresses due to depth-averaging are neglected. The computed water depth in the channel is compared with experimental data obtained by Mizumura. The effect of bottom friction, effective stresses, artificial viscosity, grid geometry, boundary conditions, and the Courant-Friedrichs-Lewy (CFL) number are investigated. Similarities and differences in the behavior of the models are observed and discussed.
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References
1.
Anderson, D. A., Tannehill, J. C., and Pletcher, R. H. (1984). Computational fluid mechanics and heat transfer, Hemisphere Publishing, New York.
2.
Beam, R. M., and Warming, R. F. (1978). “An implicit factored scheme for the compressible Navier-Stokes equations.” AIAA J., 16(4), 393–402.
3.
Bhallamudi, S. M., and Chaudhry, M. H. (1992). “Computations of flow in open-channel transitions.”J. Hydr. Res., 30(1), 225–252.
4.
Chaudhry, M. H. (1993). Open-channel flow, Prentice-Hall, Englewood Cliffs, N.J.
5.
Dammuler, D. C., Bhallamudi, S. M., and Chaudhry, M. H. (1989). “Modeling of unsteady flow in curved channel.”J. Hydr. Engrg., ASCE, 115(11), 1470–1495.
6.
Fennema, R. J., and Chaudhry, M. H. (1990). “Explicit methods for 2-D transient free-surface flows.”J. Hydr. Engrg., ASCE, 116(8), 1013–1034.
7.
Jiminez, O. F., and Chaudhry, M. H. (1988). “Computations of supercritical free-surface flows.”J. Hydr. Engrg., ASCE, 114(4), 377–395.
8.
Kuipers, J., and Vreugdenhil, C. B. (1973). “Calculations of two-dimensional horizontal flow.” Rep. No. S163, Part I, Delft Hydraulics Lab, Delft, The Netherlands.
9.
MacCormack, R. W. (1969). “The effect of viscosity in hypervelocity impact cratering.” Paper 69-354, American Institute of Aeronautics and Astronautics, Cincinnati, Ohio.
10.
Mizumura, K. (1995). “Free-surface profile of open-channel flow with wavy boundary.”J. Hydr. Engrg., ASCE, 121(7), 533–539.
11.
Molls, T. R. ( 1992). “A general 2D free-surface flow model for solving the depth-averaged equations using an implicit ADI scheme.” PhD thesis, Washington State University, Pullman, Wash.
12.
Molls, T. R., and Chaudhry, M. H. (1995). “Depth-averaged open-channel flow model.”J. Hydr. Engrg., ASCE, 121(6), 453–465.
13.
Molls, T. R., Chaudhry, M. H., and Khan, K. W. (1995). “Numerical simulation of two-dimensional flow near a spur-dike.” Adv. in Water Resour., 18(4), 227–236.
14.
Molls, T. R., Zhao, G., and Molls, F. B. (1998). “Friction slope in depth-averaged flow.”J. Hydr. Engrg., ASCE, 124(1), 81–85.
15.
Steger, J. L. (1978). “Implicit finite-difference simulation of flow about arbitrary two-dimensional geometries.” AIAA J., 16(7), 679–686.
16.
Towne, C. E., Schwab, J. R., and Bui, T. T. (1993). PROTEUS two-dimensional Navier-Stokes computer code—version 2.0.” NASA Tech. Memo. 106336, NASA Lewis Research Center, Cleveland, Ohio.
17.
Ye, J., and McCorquodale, J. A. (1997). “Depth-averaged hydrodynamic model in curvilinear collocated grid.”J. Hydr. Engrg., ASCE, 123(5), 380–388.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 126 • Issue 6 • June 2000
Pages: 437 - 445
History
Received: Nov 11, 1997
Published online: Jun 1, 2000
Published in print: Jun 2000
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