Well-balanced scheme between flux and source terms for computation of shallow-water equations over irregular bathymetry

Journal of Engineering Mechanics

Volumn 134, Issue 4, 2008, Pages 277-290

  Kim, Dae Hong ^a   Cho, Yong Sik ^b   Kim, Hyung Jun ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b Hanyang University   (South Korea)

Author keywords

Bathymetry; Computation; Numerical models; Shallow waters; Subcritical flow; Supercritical flow

Indexed keywords

BATHYMETRY; DAMS; GRADIENT METHODS; MATHEMATICAL MODELS;

HYPERBOLIC-TYPE SHALLOW-WATER EQUATIONS; RIEMANN SOLVERS; SHALLOW-WATER EQUATIONS; SUPERCRITICAL FLOWS;

FLOW OF WATER;

BATHYMETRY; DAMS; FLOW OF WATER; GRADIENT METHODS; MATHEMATICAL MODELS;

ACCURACY ASSESSMENT; BATHYMETRY; DAM FAILURE; EXPERIMENTAL STUDY; LABORATORY METHOD; NUMERICAL METHOD; NUMERICAL MODEL; SHALLOW-WATER EQUATION; STEADY FLOW; SUPERCRITICAL FLOW;

EID: 41049113279     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(2008)134:4(277)     Document Type: Article

References (20)

1. Bermudez, A., and Vazquez, M. E. (1994). "Upwind methods for hyperbolic conservation laws with source terms." Comput. Fluids CPFLBI0045-793010.1016/0045-7930(94)90004-3, 23(8), 1049-1071.
2. Birman, A., and Falcovitz, J. (2006). "Application of the GRP scheme to open channel flow equations." J. Comput. Phys. JCTPAH0021-9991, 10.1016/j.jcp.2006.07.008in press.
3. Bradford, S. F., and Sanders, B. F. (2002). "Finite-volume model for shallow-water flooding of arbitrary topography." J. Hydraul. Eng. JHEND80733-942910.1061/(ASCE)0733-9429(2002)128:3(289), 128(3), 289-298.
4. Chow, V. T. (1959). Open-channel hydraulics, McGraw-Hill, Kogakusha.
5. Garcia, P., and Vazquez, M. E. (2000). "On numerical treatment of the source terms in the shallow water equations." Comput. Fluids CPFLBI0045-793010.1016/S0045-7930(99)00038-9, 29(8), 951-979.
6. Hu, K., Mingham, C. G., and Causon, D. M. (2000). "Numerical simulation of wave overtopping of coastal structures using the nonlinear shallow water equations." Coastal Eng. COENDE0378-383910.1016/ S0378-3839(00)00040-5, 41(4), 433-465.
7. Hubbard, M. E., and Garcia, P. (2000). "Flux difference splitting and the balancing of source terms and flux gradients." J. Comput. Phys. JCTPAH0021-999110.1006/jcph.2000.6603, 165(1), 89-125.
8. Kim, D. H., Cho, Y. S., and Kim, W. G. (2004). "WAF-type scheme for shallow-water equations with fractional step method." J. Eng. Mech. JENMDT0733-939910.1061/(ASCE)0733-9399(2004)130:2(152), 130(2), 152-160.
9. Morris, M. (2000). "CADAM: Concerted action on dambreak modeling-Final report." Rep. No. SR 571, HR Wallingford.
10. Morris, M. (2001). "CADAM-EU converted action on dam break modelling." 〈http://www.hrwallingford.co.uk/projects/CADAM/ 〉.
11. Nelida, C. Z., Vukovic, S., and Sopta, L. (2004). "Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations." J. Comput. Phys. JCTPAH0021-9991, 200(2), 512-548.
12. Synolakis, C. E. (1987). "The runup of solitary waves." J. Electrocardiol. JECAB40022-0736, 185, 523-545.
13. Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, New York.
14. Vukovic, S., and Sopta, L. (2002). "ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations." J. Comput. Phys. JCTPAH0021-9991, 179(2), 593-621.
15. Watson, G., Peregrine, D. H., and Toro, E. F. (1992). "Numerical solution of the shallow water equations on a beach using the weighted average flux method." Computational fluid dynamics, C. Hirsch, ed., Vol. 1, Elsevier, New York.
16. Wen, X. (2006). "A steady state capturing and preserving method for computing hyperbolic systems with geometrical source terms having concentrations." J. Comput. Phys. JCTPAH0021-9991, 219, 322-390.
17. Zanuttigh, B., and Lamberti, A. (2002). "Roll waves simulation using shallow water equations and weighted average flux method." J. Hydraul. Res. JHYRAF0022-1686, 40(5), 610-622.
18. Zhou, J. G., Causon, D. M., Ingram, D. M., and Mingham, C. G. (2002). "Numerical solutions of the shallow water equations with discontinuous bed topography." Int. J. Numer. Methods Fluids IJNFDW0271-209110.1002/fld.243, 38, 769-788.
19. 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. JCTPAH0021-999110.1006/jcph.2000.6670, 168(1), 1-25.
20. Zhou, J. G., Causon, D. M., Mingham, C. G., and Ingram, D. M. (2004). "Numerical prediction of dam-break flows in general geometries with complex bed topography" J. Hydraul. Eng. JHEND80733-942910.1061/ (ASCE)0733-9429(2004)130:4(332), 130(4), 332-340.