Finite Volume Model for Shallow Water Equations with Improved Treatment of Source Terms

Journal of Hydraulic Engineering

Volumn 134, Issue 2, 2008, Pages 231-242

  Kuiry, Soumendra Nath ^a   Pramanik, Kiran ^b   Sen, Dhrubajyoti ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

^b Central Water Commission India   (India)

Author keywords

Grid systems; India; Numerical models; Shallow water; Tidal currents; Topography; Unsteady flow

Indexed keywords

EQUATIONS OF MOTION; OCEAN CURRENTS; TOPOGRAPHY; APPROXIMATION THEORY; FINITE VOLUME METHOD; MATHEMATICAL MODELS; TIDES; UNSTEADY FLOW;

BED SLOPE; FINITE VOLUME MODELING; FLUX GRADIENTS; GRID SYSTEMS; INDIA; SHALLOW WATER EQUATIONS; SHALLOW WATERS; SIMPLE++; SOURCE TERMS; TIDAL CURRENTS;

NUMERICAL MODELS; OCEAN CURRENTS;

GODUNOV-TYPE UPWIND FINITE VOLUME FORMULATION; ROE'S APPROXIMATE RIEMANN SOLVER; SECOND-ORDER SPATIAL ACCURACY; SHALLOW WATER EQUATION;

APPROXIMATION THEORY; FINITE VOLUME METHOD; MATHEMATICAL MODELS; OCEAN CURRENTS; TIDES; UNSTEADY FLOW;

FINITE VOLUME METHOD; NUMERICAL MODEL; SHALLOW WATER; SHALLOW-WATER EQUATION; TIDAL CURRENT;

ASIA; EURASIA; HOOGHLY RIVER; INDIA; SOUTH ASIA; WEST BENGAL;

EID: 38349156657     PISSN: 07339429     EISSN: 19437900     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9429(2008)134:2(231)     Document Type: Article

References (49)

1. Akanbi, A. A., and, Katapodes, N. D. (1988). " Model for flood propagation on initially dry land." J. Hydraul. Eng. JHEND8 0733-9429, 114 (7), 689-706.
2. Alcrudo, F., and, García-Navarro, P. (1993). " A high-resolution Godunov-type scheme in finite volumes for the 2D shallow water equations." Int. J. Numer. Methods Fluids IJNFDW 0271-2091, 16, 489-505. 10.1002/fld.1650160604
3. Alcrudo, F., García-Navarro, P., and, Saviron, J. (1992). " Flux difference splitting for 1D open channel flow equations." Int. J. Numer. Methods Fluids IJNFDW 0271-2091, 14, 1009-1018. 10.1002/fld.1650140902
4. Anastasiou, K., and, Chan, C. T. (1997). " Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes." Int. J. Numer. Methods Fluids IJNFDW 0271-2091, 24, 1225-1245. 10.1002/(SICI)1097-0363(19970615)24:11<1225::AID-FLD540>3.0.CO;2-D
5. Beffa, C. (1994). " Practische lösung der tiefengemittelten flachwasser gleichungen." Communication No. 133, Lab of Hydr., ETH Zürich, Zürich.
6. Beffa, C., and, Connell, R. J. (2001). " Two-dimensional flood plain flow. I: Model description." J. Hydrol. Eng. JHYEFF 1084-0699, 6 (5), 397-405. 10.1061/(ASCE)1084-0699(2001)6:5(397)
7. Berger, R. C., and, Stockstill, R. L. (1995). " Finite-element model for high-velocity channels." J. Hydraul. Eng. JHEND8 0733-9429, 121 (10), 710-716. 10.1061/(ASCE)0733-9429(1995)121:10(710)
8. Bermúdez, A., Dervieux, A., Desideri, J. A., and, Vazquez-Cendón, M. E. (1998). " Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes." Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825, 155, 49-72. 10.1016/S0045-7825(97)85625-3
9. Bermúdez, A., and, Vázquez-Cendón, M. E. (1994). " Upwind methods for hyperbolic conservation laws with source terms." Comput. Fluids CPFLBI 0045-7930, 23 (8), 1049-1071. 10.1016/0045-7930(94)90004-3
10. Bradford, S. F., and, Sanders, B. F. (2002). " Finite volume model for shallow-water flooding of arbitrary topography." J. Hydraul. Eng. JHEND8 0733-9429, 128 (3), 289-298. 10.1061/(ASCE)0733-9429(2002)128:3(289)
11. Brufau, P., and, García-Navarro, P. (2003). " Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique." J. Comput. Phys. JCTPAH 0021-9991, 186, 503-526. 10.1016/S0021-9991(03)00072-X
12. Brufau, P., Vázquez-Cendón, M. E., and, García-Navarro, P. (2002). " A numerical model for the flooding and drying of irregular domains." Int. J. Numer. Methods Fluids IJNFDW 0271-2091, 39, 247-275. 10.1002/fld.285
13. Burguete, J., and, García-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 IJNFDW 0271-2091, 37, 209-248. 10.1002/fld.175
14. Chaudhry, M. H. (1994). Open-channel flow, Prentice-Hall of India Pvt. Ltd., New Delhi, India.
15. Chow, V. T. (1973). Open channel hydraulics, McGraw-Hill, New York.
16. Cunge, J. A., Holly, F. M., and, Verwey, A. (1980). Practical aspects of computational river hydraulics, Pitman Publishing Limited, London.
17. Delis, A. I., Skeels, C. P., and, Ryrie, S. C. (2000). " Evaluation of some approximate Riemann solvers for transient open channel flows." J. Hydraul. Res. JHYRAF 0022-1686, 38 (3), 217-231.
18. Farshi, D., and, Komaei, S. (2005). " Discussions of finite volume method for two-dimensional shallow water flows on unstructured grids by Tae Hoon Yoon and Seok-koo Kang." J. Hydraul. Eng. JHEND8 0733-9429, 130 (7), 678-688. 10.1061/(ASCE)0733-9429(2004)130:7(678)
19. Fennema, R. J., and, Chaudhry, M. H. (1990). " Explicit methods for 2-D transient free-surface flows." J. Hydraul. Eng. JHEND8 0733-9429, 116 (8), 1013-1034. 10.1061/(ASCE)0733-9429(1990)116:8(1013)
20. García-Navarro, P., and, Vázquez-Cendón, M. E. (2000). " On numerical treatment of the source terms in shallow water equations." Comput. Fluids CPFLBI 0045-7930, 29 (8), 951-979. 10.1016/S0045-7930(99)00038-9
21. Glaister, P. (1988). " Approximate Riemann solutions of the shallow water equations." J. Hydraul. Res. JHYRAF 0022-1686, 26 (3), 293-306.
22. Goutal, N., and, Maurel, F. (1997). Technical Rep. No. HE-43/97/016/A, Electricité de France, Département Laboratoire National d'hydraulique, France.
23. Hirsch, C. (1988). Numerical computation of internal and external flows, Vol. II, Wiley, New York.
24. Holmes, D. G., and, Connel, S. D. (1989). " Solution of the 2D Navier Stokes equations on unstructured adaptive grids." Proc., AIAA 9th CFD Conf., AIAA Paper No. 89-1932.
25. Hubbard, M. E. (1999). " Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids." J. Comput. Phys. JCTPAH 0021-9991, 155, 54-74. 10.1006/jcph.1999.6329
26. Hubbard, M. E., and, García-Navarro, P. (2000). " Flux difference splitting and the balancing of source terms and flux gradients." J. Comput. Phys. JCTPAH 0021-9991, 165 (1), 89-125. 10.1006/jcph.2000.6603
27. Jawahar, P., and, Kamath, H. (2000). " A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids." J. Comput. Phys. JCTPAH 0021-9991, 164, 165-203. 10.1006/jcph.2000.6596
28. Katapodes, N. D., and, Strelkoff, R. (1978). " Computing two-dimensional dam-break flood waves." J. Hydr. Div. JYCEAJ 0044-796X, 104 (9), 1269-1288.
29. Komaei, S., and, Bechteler, W. (2004). " An improved, robust implicit solution for the two-dimensional shallow water equations on unstructured grids." Proc., 2nd Int. Conf. on Fluvial Hydraulics, Vol. 2, M. Greco., ed., Balkema, Rotterdam, The Netherlands, 1065-1072.
30. LeVeque, R. J. (1998). " Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave propagation algorithm." J. Comput. Phys. JCTPAH 0021-9991, 146, 346-365. 10.1006/jcph.1998.6058
31. Molls, T., and, Chaudhry, M. H. (1995). " Depth-averaged open-channel flow model." J. Hydraul. Eng. JHEND8 0733-9429, 121 (6), 453-465. 10.1061/(ASCE)0733-9429(1995)121:6(453)
32. Nujic, M. (1995). " Efficient implementation of nonoscillatory schemes for the computation of free surface flow." J. Hydraul. Res. JHYRAF 0022-1686, 33 (1), 101-111.
33. Roberts, S., and, Zoppou, C. (2000). " Robust and efficient solution of the 2D shallow water equation with domains containing dry beds." http:://anziam.austms.org.au/V42/CTAC99/Robe »(Feb. 10, 2003).
34. Roe, P. L. (1981). " Approximate Riemann solvers, parameter vectors and difference schemes." J. Comput. Phys. JCTPAH 0021-9991, 43, 357-372. 10.1016/0021-9991(81)90128-5
35. Roe, P. L. (1986). " A basis for upwind differencing of the two-dimensional unsteady Euler equations." Numerical methods for fluid dynamics II, Oxford Univ. Press, Oxford, U.K.
36. Sanders, B. F. (2001). " High-resolution and nonoscillatory solution of the St. Venant equations in nonrectangular and nonprismatic channels." J. Hydraul. Res. JHYRAF 0022-1686, 39 (3), 321-330.
37. Shewchuk, J. R. (1996). " Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator." Lect. Notes Comput. Sci. LNCSD9 0302-9743 1148, 203-222, http://www-2.cs.cmu.edu/~quake/triangle.html .
38. Sleigh, P. A., Berzins, M., Gaskell, P. H., and, Wright, N. G. (1998). " An unstructured finite-volume algorithm for predicting flow in rivers and estuaries." Comput. Fluids CPFLBI 0045-7930, 27 (4), 479-508. 10.1016/S0045-7930(97)00071-6
39. Spekreijse, S. P. (1988). " Multigrid solution of steady Euler equations." CWI Tract No. 46, Amsterdam, The Netherlands.
40. Tan, W. (1992). Shallow water hydrodynamics, Elsevier, Amsterdam, The Netherlands.
41. Tucciarelli, T., and, Termini, D. (2000). " Finite-element modelling of floodplain flow." J. Hydraul. Eng. JHEND8 0733-9429, 126 (6), 416-424. 10.1061/(ASCE)0733-9429(2000)126:6(416)
42. Valiani, A., and, Begnudelli, L. (2006). " Divergence form of bed slope source term in shallow water equations." J. Hydraul. Eng. JHEND8 0733-9429, 132 (7), 652-665. 10.1061/(ASCE)0733-9429(2006)132:7(652)
43. Valiani, A., Caleffi, V., and, Zanni, A. (2002). " Case study: Malpasset dam-break simulation using two-dimensional finite volume method." J. Hydraul. Eng. JHEND8 0733-9429, 128 (5), 460-472. 10.1061/(ASCE)0733-9429(2002)128:5(460)
44. Vázquez-Cendón, M. E. (1999). " Improved treatment of source terms in upwind schemes for the shallow water equations." J. Comput. Phys. JCTPAH 0021-9991, 148, 497-526. 10.1006/jcph.1998.6127
45. Wang, J.-W., and, Liu, R.-X. (2000). " A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water problems." Math. Comput. Simul. MCSIDR 0378-4754, 53, 171-184. 10.1016/S0378-4754(00)00173-7
46. Yoon, T. H., and, Kang, S. K. (2004). " Finite volume model for two-dimensional shallow water flows on unstructured grids." J. Hydraul. Eng. JHEND8 0733-9429, 130 (7), 678-688. 10.1061/(ASCE)0733-9429(2004)130:7(678)
47. Zhao, D. H., Shen, H. W., Lai, J. S., and, Tabios, G. Q., III. (1996). " Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling." J. Hydraul. Eng. JHEND8 0733-9429, 122 (12), 692-702. 10.1061/(ASCE)0733-9429(1996)122:12(692)
48. Zhao, D. H., Shen, H. W., Tabios, G. Q., III, Lai, J. S., and, Tan, W. Y. (1994). " A finite-volume two-dimensional unsteady flow model for river basins." J. Hydraul. Eng. JHEND8 0733-9429, 120 (7), 863-883. 10.1061/(ASCE)0733-9429(1994)120:7(863)
49. 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. JCTPAH 0021-9991, 168, 1-25. 10.1006/jcph.2000.6670