Modeling 3D Supercritical Flow with Extended Shallow-Water Approach

Journal of Hydraulic Engineering

Volumn 132, Issue 9, 2006, Pages 916-926

  Krüger, Susanne ^a,b   Rutschmann, Peter ^b,c  

^a Sulzer Ltd   (Switzerland)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Computational fluid dynamics technique; Finite element method; Shallow water; Shock waves; Supercritical flow; Three dimensional models

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; DISTRIBUTION FUNCTIONS; EQUATIONS OF MOTION; SHOCK WAVES; CHANNEL FLOW; COMPUTER SIMULATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PRESSURE DISTRIBUTION;

CHANNEL TRANSITION; COMPUTATIONAL FLUID DYNAMICS TECHNIQUE; FLOW IN CHANNELS; HIGH-ORDER; SHALLOW WATER APPROACH; SHALLOW WATER EQUATIONS; SHALLOW WATERS; SHOCK-WAVES; SUPERCRITICAL FLOW; THREE DIMENSIONAL MODELLING;

FINITE ELEMENT METHOD; COMPUTATIONAL FLUID DYNAMICS;

SHALLOW WATER; SUPERCRITICAL FLOW; THREE-DIMENSIONAL MODELS;

CHANNEL FLOW; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PRESSURE DISTRIBUTION; SHOCK WAVES;

COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; SHALLOW-WATER EQUATION; SHOCK WAVE; SUPERCRITICAL FLOW; THREE-DIMENSIONAL MODELING;

EID: 33747347495     PISSN: 07339429     EISSN: 19437900     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9429(2006)132:9(916)     Document Type: Article

References (39)

1. Abbott, M. B. (1979). "Computational hydraulics, elements of the theory of free surface flows." Monographs and surveys in water resources engineering, Vol. 1, Pitman, London.
2. Abbot, M. B., McCowan, A. D., and Warren, I. R. (1984). "Accuracy of short-wave numerical models." J. Hydraul. Eng., 110(10), 1287-1301.
3. Abbot, M. B., and Verwey, A. (1970). "Four-point method of characteristics." J. Hydraul. Div., Am. Soc. Civ. Eng., 96(12), 2549-2564.
4. Bagge, G., and Herbich, J. B. (1967). "Transitions in supercritical open-channel flow." J. Hydraul. Div., Am. Soc. Civ. Eng., 93(5), 23-41.
5. Beffa, C. J. (1994). "Praktische Lösung der tiefengemittelten Flach-wassergleichungen." Ph.D.Thesis No. 10870, ETH Zurich, Zurich, Switzerland (in German).
6. Berger, R. C., and Stockstill, R. L. (1995). "Finite-element model for high-velocity channels." J. Hydraul. Eng., 121(10), 710-716.
7. Bhallamudi, S. M., and Chaudhry, M. H. (1992). "Computation of flows in open-channel transitions." J. Hydraul. Res., 30(1), 77-93.
8. Brooks, A. N, and Hughes, T. J. R. (1982). "Streamline upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations." Comput. Methods Appl. Mech. Eng., 32, 199-259.
9. Causon, D. M., Mingham, C. G., and Ingram, D. M. (1999). "Advances in calculation methods for supercritical flow in spillway channels." J. Hydraul. Eng., 125(10), 1039-1050.
10. Ellis, J. (1970). "Unsteady flow in channel of variable cross section." J. Hydraul. Div., Am. Soc. Civ. Eng., 96(10), 1927-1945.
11. Evangelisti, G. (1966). "Mathematical models of open-channel flow." Surface hydrodynamics, NATO Advanced Study Institute, Bressano, Italy, 198-283.
12. Fennema, R. F, and Chaudhry, M. H. (1987). "Simulation of one-dimensional dam-break flows." J. Hydraul. Res., 25(1), 41-51.
13. Fennema, R. F, and Chaudhry, M. H. (1989). "Implicit methods for two-dimensional unsteady free-surface flows." J. Hydraul. Res., 27(3), 321-332.
14. Hager, W. H. (1989). "Supercritical flow in channel junctions." J. Hydraul. Eng., 115(5), 595-616.
15. Hirt, C. W., and Nichols, B. D. (1981). "Volume of fluid (VOF) method for the dynamics of free boundaries." J. Comput. Phys., 39, 201-225.
16. Hughes, T. J. R., and Brooks, A. N. (1979). "A multidimensional upwind scheme with no crosswind diffusion." Finite elements for convection dominated flows, T. J. R Hughes, ASME.
17. Hughes, T. J. R., Franca, L. P., and Hulbert, G. M. (1989). "A new finite element formulation for computational fluid dynamics. VIII: The Galerkin/least-squares method for advective-diffusive systems." Com-put. Methods Appl. Mech. Eng., 73, 173-189.
18. Hughes, T. J. R., Liu, W. K., and Zimmermann, T. K. (1981). "Lagrangian-Eulerian finite-element formulation for incompressible viscous flows." Comput. Methods Appl. Mech. Eng., 29, 329-349.
19. Ippen, A. T., and Dawson, J. H. (1951). "Design of channel contractions." Symp., High-Velocity Flow in Open Channels, 116, 326-446.
20. Jiménez, O. F., and Chaudhry, M. H. (1988). "Computation of supercritical free-surface flows." J. Hydraul. Eng., 114(4), 377-395.
21. Katopodes, N. D. (1984a). "Dissipative Galerkin scheme for open-channel flow." J. Hydraul. Eng., 110(4), 450-466.
22. Katopodes, N. D. (1984b). "Two-dimensional surges and shocks in open channels." J. Hydraul. Eng., 110(6), 794-812.
23. Katopodes, N. D., and Wu, C.-T. (1986). "Explicit computation of discontinuous channel flow." J. Hydraul. Eng., 112(6), 456-475.
24. Khan, A. A., and Steffler, P. M. (1996). "Vertically averaged and moment equations model for flow over curved beds." J. Hydraul. Eng., 122(1), 3-9.
25. Kröger, S. (2000). "Computational contribution to highly supercritical flows." Ph.D.Thesis No. 13838, ETH Zurich, Zurich, Switzerland.
26. Kröger, S., Börgisser, M. F., and Rutschmann, P. (1998). "Advances in calculating supercritical flows in spillway contractions." Hydroinfor-matics 98, V. Babovic and L. C. Larsen, eds., Vol. 1, 163-170.
27. Liggett, J. A., and Vasudev, S. U. (1965). "Slope and friction effects in two-dimensional high speed channel flow." 11th IAHR Congress, Leningrad, Vol. 1, Rep. No. 1.25.
28. Liggett, J. A., and Woolhiser, D. A. (1967). "Difference solutions of the shallow-water equation." J. Eng. Mech. Div., Am. Soc. Civ. Eng., 93(2), 39-71.
29. Mazumder, S. K, and Hager, W. H. (1993). "Supercritical expansion flow in Rouse modified and reversed transitions." J. Hydraul. Eng., 119(2), 201-219.
30. Näf, D. (1996). "Numerische Simulationen von Stosswellen in Freispie-gelströmungen." Ph.D.Thesis No. 11968, ETH Zurich, Zurich, Switzerland (in German).
31. Preissman, A. (1971). "Modèles pour le calcul de la propagation des crues." La Houille Blanche, 26(3), 219-224 (in French).
32. Rahman, M., and Chaudhry, M. H. (1997). "Computation of flow in open-channel transitions." J. Hydraul. Res., 35(2), 243-256.
33. Rutschmann, P. (1993). "Fe solver with 4D finite elements in space and time." FE in Fluids, Proc, VIII. Int. Conf. On FE in Fluid, Barcelona, K Morgan, K Oñate, J. Periaux, J. Peraire and O. C. Zienkiewicz, eds., 136-144.
34. Rutschmann, P. (1994). "Obtaining higher order accuracy with linear shape functions-A new approach for transient problems." Comput. Fluid Dyn., 94 Ed., Wagner, Hirschel, Periaux, and Riva, 165-169.
35. Sethian, J. A. (1996). "Level set methods: Evolving interfaces in geometry, fluid mechanics, computer vision, and materials science." Cambridge University Press, Cambridge, U.K.
36. Steffler, P. M., and Jin, Y.-C. (1993). "Depth-Averaged and moment equations for moderately shallow free surface flow." J. Hydraul. Res., 21(1), 5-17.
37. Von Kármán, T. (1938). "Eine praktische Anwendung der Analogie zwis-chen Ueberschallströmungen in Gasen und öberkritischer Strömung in offenen Gerinnen." ZAMM, 18 Feb., 49-56.
38. Vreugdenhil, C. B. (1994). "Numerical methods for shallow-water flow." Water sci.Technol, Vol. 13, Kluwer Academic, Dordrecht.
39. Zienkiewicz, O. C. (1971). "The finite-element method in engineering science." 2nd Ed., McGraw-Hill, New York.