Upwind conservative scheme for the Saint Venant equations

Journal of Hydraulic Engineering

Volumn 130, Issue 10, 2004, Pages 977-987

  Ying, Xinya ^a   Khan, Abdul A ^b   Wang, Sam S Y ^a  

^a UNIVERSITY OF MISSISSIPPI   (United States)

^b AMRL   (United States)

Author keywords

Dam failure; Numerical models; Open channels; Unsteady flow

Indexed keywords

HYDRAULIC JUMP; ROBUSTNESS (CONTROL SYSTEMS); VISCOSITY; VOLUME MEASUREMENT; WATER; DAMS; NUMERICAL METHODS; STATISTICAL METHODS;

HYDRAULIC JUMPS; OPEN WATER-SURFACE-GRADIENT APPROACH; UPWIND CONSERVATION; CONSERVATIVE SCHEMES; DAM FAILURE; DAM-BREAK PROBLEMS; GRADIENT APPROACH; ONE-DIMENSIONAL; OPEN CHANNELS; OPEN-CHANNEL FLOW; SAINT VENANT EQUATION; WATER SURFACE GRADIENT; WEIGHTED AVERAGES;

CHANNEL FLOW; OPEN CHANNEL FLOW;

FLOW MODELING; HYDRAULIC JUMP; OPEN CHANNEL FLOW; UNSTEADY FLOW;

CHANNEL HYDRAULICS; FLOW MODELING; OPEN CHANNEL FLOW; UNSTEADY FLOW;

CHRISTIA;

EID: 8744229099     PISSN: 07339429     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. Bradford, S. F., and Sanders, B. F. (2002). "Finite-volume model for shallow-water flooding of arbitrary topography." J. Hydraul. Eng. 128(3), 289-298.
2. Burguete, J., and Garcia-Navarro, P. (2001). "Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows." Int. J. Numer. Methods Fluids, 37, 209-248.
3. Delis, A. I., and Skeels, C. P. (1998). "TVD schemes for open channel flow." Int. J. Numer. Methods Fluids, 26, 791-809.
4. Garcia-Navarro P., Alcrudo F., and Saviron J. M. (1992). "1-D open channel flow simulation using TVD-McCormack scheme." J. Hydraul. Eng., 118(10), 1359-1372.
5. Garcia-Navarro P., and Vazquez-Cendon M. E. (2000). "On numerical treatment of the source terms in the shallow water equations." Comput. Fluids, 29, 951-979.
6. Gharangik, A. M., and Chaudhry, M. H. (1991). "Numerical simulation of hydraulic jump." J. Hydraul. Eng., 117(9), 1195-1211.
7. Goutal, N., and Maurelz, F. (1997). Proc., 2nd Workshop on Dam-Break Wave Simulation. Rep. LNH HE-43/97/016/B, National Hydraulic Laboratory, France.
8. Henderson, F. M. (1966). Open channel flow, McGraw-Hill, New York.
9. Jha, A. K., Akiyama, J., and Ura, M. (2000) "Flux-difference splitting schemes for 2D flood flows." J. Hydraul. Eng., 126(1), 33-42.
10. Jin, M., and Fread, D. L. (1997). "Dynamic flood routing with explicit and implicit numerical solution schemes." J. Hydraul. Eng., 123(3), 166-173.
11. Khan, A. A. (2000). "Modeling flow over an initially dry bed." J. Hydraul. Res., 38(5), 383-388.
12. LeVeque, R. J. (1998). "Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm." J. Comput. Phys., 146, 346-365.
13. Louaked, M., and Hanich, L. (1998). "TVD scheme for the shallow water equations." J. Hydraul. Res., 36(3), 363-378.
14. Mingham, C. G., and Causon, D. M. (1998). "High-resolution finite-volume method for shallow water flows." J. Hydraul. Eng., 124(6), 605-614.
15. Molls, T., and Molls, F. (1998).Space-time conservation method applied to Saint Venant equations." J. Hydraul. Eng., 124(5), 501-508.
16. Nujic, M. (1995). "Efficient implementation of non-oscillatory schemes for the computation of free-surface flows." J. Hydraul. Res., 33(1), 100-111.
17. Rosu, C., and Ahmed, M. (1999). "Toce River dam-break test case-A comparison between the ISIS numerical model and the physical model." Proc., 3rd CADAM Workshop, Milan, Italy.
18. Sanders, B. F. (2001). "High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and non-prismatic channels." J. Hydraul. Res., 39(3), 321-330.
19. Savic, L. J., and Holly, F. M., Jr. (1993). "Dambreak flood waves computed by modified Godunov method." J. Hydraul. Res., 31(2 , 187-204.
20. Soares Frazao, S., and Zech, Y. (1999). "Computation of extreme flood flow through the Toce Valley." Proc., 3rd CADAM Workshop Milan, Italy.
21. Soares Frazao, S., and Zech, Y. (2002). "Dam break in channels with 90° bend." J. Hydraul. Eng., 128(11), 956-968.
22. Soares Frazao, S. , Morris, M., and Zech, Y. (2000). "CADAM Project." (CD-ROM), Hydraulics Division, Civil Engineering Dept., Univ. Catholique de Louvain, Belgium.
23. Sod, G. A. (1978). "A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws." J. Comput. Phys. 27, 1-31.
24. Tseng, M. H. (2000). "Two-dimensional shallow water flows simulation using TVD-MacCormac scheme." J. Hydraul. Res., 38(2), 123-131.
25. Toro, E. F. (1997). Riemann solvers and numerical methods for fluid dynamics, Springer, New York.
26. Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, New York.
27. Valiani, A., Caleffi, V., and Zanni, A. (2002). "Case Study: Malpasset dam-break simulation using a two-dimensional finite volume method." J. Hydraul. Eng., 128(5), 460-472.
28. Vazquez-Cendon, M. E. (1999). "Improved treatment of source terms in upwind schemes for shallow water equations in channels with irregular geometry." J. Comput. Phys., 148, 497-526.
29. Wang, J. S., Ni, H. G., and He, Y. S. (2000). "Finite-difference TVD scheme for computation of dam-break problems." J. Hydraul. Eng., 126(4), 253-262.
30. Waterways Experiment Station (WES). (1960). "Floods resulting from suddenly breached dams." Miscellaneous Paper No.2-374, Rep. 1: Conditions of Minimum Resistance, U.S. Army Corps of Engineers, Vicksburg, Miss.
31. Yang, J. Y., Hsu, C. A., and Chang, S. H. (1993). "Computations of free surface flows. Part 1: One-dimensional dam-break flow." J. Hydraul. Res., 31(1), 19-34.
32. Ying, X., Akiyama, J., and Ura, M. (1999). "Motion of dense fluid released into quiescent water with finite depth." J. Hydraul., Coastal Environmental Eng., 635/II-49, 141-152.
33. Zhao, D. H., Shen, H. W., Lai, J. S., and Tabios, III, G. Q. (1996). "Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling." J. Hydraul. Eng., 122(12), 692-702.
34. Zhou, J. G., Causon, D. M., Mingham, C. G., and Ingram, D. M. (2001). "The surface gradient method for the treatment of source terms in the shallow-water equations." J. Comput. Phys., 168, 1-25.
35. Zoppou, C., and Roberts, S. (2003). "Explicit schemes for dam-break simulations." J. Hydraul. Eng., 129(1), 11-34.