Simple Curvilinear Method for Numerical Methods of Open Channels
Publication: Journal of Hydraulic Engineering
Volume 127, Issue 11
Abstract
Three-dimensional finite-difference or finite-volume models of sinuous open channels (e.g., narrow rivers, estuaries, and reservoirs) generally require boundary-fitted grids and curvilinear flow solution. Cartesian models with square grid cells are simpler to apply, but require a larger number of cells, as the cell size is determined by cross-stream resolution. This paper presents a simplified curvilinear approach suitable for systems where the along-stream length scale is larger than the cross-stream scale. The curvilinear Navier-Stokes equations are manipulated so the left-hand side is identical to the Cartesian momentum equations. The right-hand side then consists of grid-stretching curvature terms. These terms are written as functions of a perturbation parameter, so the first-order curvilinear effects are obtained with the lowest-order perturbation terms. As the Cartesian equations' form is preserved, we can readily adapt a Cartesian model to this perturbation curvilinear approach by adding the small curvilinear terms as explicit momentum sources.
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References
1.
Aris, R. ( 1962). Vectors, tensors, and the basic equations of fluid mechanics, Dover, New York.
2.
Casulli, V., and Cheng, R. T. ( 1992). “Semi-implicit finite difference methods for three-dimensional shallow water flow.” Int. J. Numer. Methods in Fluids, 15(6), 629–648.
3.
Chow, V. T. ( 1973). Open-channel hydraulics, McGraw-Hill, New York.
4.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. ( 1979). Mixing in inland and coastal waters, Academic Press, San Diego.
5.
Goncharov, V. N. ( 1964). Dynamics of channel flow, Israel Program for Scientific Translations, Jerusalem.
6.
Hodges, B. R. ( 2000a). “Derivation of perturbation curvilinear methods.” Tech. Rep. WP 1423 BH, Ctr. for Water Res., University of Western Australia, Nedlands, Australia.
7.
Hodges, B. R. ( 2000b). “Numerical techniques in CWR-ELCOM.” Tech. Rep. WP 1422 BH, Ctr. for Water Res., University of Western Australia, Nedlands, Australia.
8.
Hodges, B. R., Imberger, J., Saggio, A., and Winters, K. B. ( 2000). “Modeling basin-scale internal waves in a stratified lake.” Limno. Oceanogr., 45(7), 1603–1620.
9.
Meakin, R. L., and Street, R. L. ( 1988). “Simulation of environmental flow problems in geometrically complex domains. Part I: A general coordinate transformation.” Comput. Methods Appl. Mech. Engrg., 68(2), 151–175.
10.
Posey, C. J. ( 1969). Fundamentals of open channel hydraulics, Rocky Mountain Hydraulic Laboratory, Allenspark, Colo.
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Received: Oct 11, 2000
Published online: Nov 1, 2001
Published in print: Nov 2001
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