Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids

International Journal for Numerical Methods in Fluids

Volumn 50, Issue 3, 2006, Pages 309-345

  Guinot, Vincent ^a   Soares Frazão, Sandra ^b  

^a CNRS   (France)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Analytical solutions; Godunov type schemes; Hyperbolic systems of conservation laws; Porosity; Riemann solver; Shallow water equations

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; ORDINARY DIFFERENTIAL EQUATIONS; POROSITY; VECTORS;

GODUNOV TYPE SCHEMES; RIEMANN SOLVER; SHALLOW WATER EQUATIONS;

FLOW OF WATER;

FLOOD PLAIN; FLOW MODELING; POROSITY; SHALLOW WATER; TWO-DIMENSIONAL FLOW;

EID: 30644467592     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1059     Document Type: Article

References (27)

1. EC Contract EVG1-CT-2001-00037 IMPACT investigation of extreme flood processes and uncertainty. Available at www.impact-project.net
2. Alcrudo F, Garcia P, Brufau P, Murillo J, Garcia D, Mulet J, Testa G, Zuccala D. The Model City Flooding Experiment. EC Contract EVG1-CT-2001-00037 IMPACT investigation of extreme flood processes and uncertainty. Proceedings of the 2nd Project Workshop, Mo i Rana, Norway, September 2002 (CD-ROM).
3. Turner-Gillespie DF, Smith JA, Bates PD. Attenuating reaches and the regional flood response of an urbanizing drainage basin. Advances in Water Resources 2003; 26:673-684.
4. Dutta D, Herath S, Musiake K. A mathematical model for flood loss estimation. Journal of Hydrology 2003; 277:24-49.
5. Vieux BE, Bedient PB. Assessing urban hydrologic prediction accuracy through event reconstruction. Journal of Hydrology, in press.
6. Campana NA, Tucci CEM. Predicting floods from urban development scenarios: case study of the Diluviao Basin,Porto Alegre, Brazil. Urban Water 2001; 3:113-124.
7. Defina A, D'Alpaos L, Mattichio B. A new set of equations for very shallow water and partially dry areas suitable to 2D numerical domains. Proceedings Specialty Conference 'Modelling of Flood Propagation over Initially Dry Areas', Milano, Italy, 29 June-1 July, 2004.
8. Hervouet J-M, Samie R, Moreau B. Modelling urban areas in dam-break flood-wave numerical simulations. Proceedings of the International Seminar and Workshop on Rescue Actions Based on Dambreak Flow Analysis, Seinâjoki, Finland, 1-6 October, 2000.
9. Godunov SK. A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics. Matematicheskii Sbornik 1959; 47:357-393.
10. Bermudez A, Vasquez-Cendron E. Upwind methods for hyperbolic conservation laws with source terms. Computers and Fluids 1994; 23:1049-1071.
11. Gallouët T, Hérard J-M, Seguin N. Some approximate Godunov schemes to compute shallow-water equations with topography. Computers and Fluids 2003; 32:479-513.
12. Bradford SF, Sanders BF. Finite-volume model for shallow-water flooding of arbitrary topography. Journal of Hydraulic Engineering 2002; 128:289-298.
13. Zhou JG, Causon DM, Mingham CG, Ingram DM. The surface gradient method for the treatment of source term in the shallow-water equations. Journal of Computational Physics 2001; 168:1-25.
14. Garcia-Navarro P, Vasquez-Cendron ME. On numerical treatment of the source terms in the shallow water equations. Computers and Fluids 2000; 29:951-979.
15. LeVeque RJ. Balancing source terms and flux gradients in high-resolution Godunov methods, the quasi-steady wave-propagation algorithm. Journal of Computational Physics 1998; 146:346-365.
16. Alcrudo F, Benkhaldoun F. Exact solutions to the Riemann problem of the shallow water equations with a bottom step. Computers and Fluids 2001; 30:643-671.
17. Harten A, Lax PD, Van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review 1987; 25:35-61.
18. Toro EF, Spruce M, Speares W. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 1994; 4:25-34.
19. Van Leer B. Toward the ultimate conservative difference scheme. IV. A new approach to numerical convection. Journal of Computational Physics 23:276-299.
20. Toro EF. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer: Berlin, 1997.
21. Guinot V. Godunov-Type Schemes, An Introduction for Engineers. Elsevier: Amsterdam, 2003.
22. Davis SF. Simplified second-order Godunov-type methods. SIAM Journal on Scientific and Statistical Computing 1988; 9:445-473.
23. Nujic M. Efficient implementation of non-oscillatory schemes for the computation of free-surface flows. Journal of Hydraulic Research 1995; 33(1):101-111.
24. Guinot V. Linear advection modelling: the issue of strongly divergent flows. Journal of Hydroinformatics 2000; 2:113-121.
25. Stoker JJR. Water Waves. Interscience: New York, 1957.
26. Cunge JA, Holly Jr FM, Verwey A. Practical Aspects of Computational River Hydraulics. Pitman Publishing: London, 1980.
27. Carlier M. Hydraulique générale et Appliquée. Eyrrolles: Paris, 1972.