Numerical boundary conditions for globally mass conservative methods to solve the shallow-water equations and applied to river flow

International Journal for Numerical Methods in Fluids

Volumn 51, Issue 6, 2006, Pages 585-615

  Burguete, J ^a   Garcia Navarro P ^a   Murillo, J ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Boundary conditions; Conservative methods; Discontinuous flow; Mass conservation; Shallow water; Source terms

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; FLOODS; MATHEMATICAL MODELS; RIVERS; WATER WAVES;

CONSERVATIVE METHODS; DISCONTINUOUS FLOW; MASS CONSERVATION; SHALLOW-WATER EQUATIONS;

FLOW OF WATER;

BOUNDARY CONDITIONS; COMPUTER SIMULATION; FLOODS; FLOW OF WATER; MATHEMATICAL MODELS; RIVERS; WATER WAVES;

EID: 33745457668     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1127     Document Type: Article

References (26)

1. Glaister P. Approximate Riemann solutions of the shallow water equations. Journal of Hydraulic Research 1988; 26:293-306.
2. García Navarro P, Vázquez Cendón ME. Some considerations and improvements on the performance of Roe's schemes for 1D irregular geometries on numerical treatment of the source terms in the shallow water equations. Computers and Fluids 2000; 126:26-40.
3. Burguete J, García Navarro P. Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows. International Journal for Numerical Methods in Fluids 2001; 37:209-248.
4. Burguete J, García Navarro P. Improving simple explicit methods for unsteady open channel and river flow. International Journal for Numerical Methods in Fluids 2004; 45:125-156.
5. Burguete J, García Navarro P. Implicit schemes with large time step for non-linear equations: application to river flow hydraulics. International Journal for Numerical Methods in Fluids 2004; 46:607-636.
6. Kreiss HO. Initial boundary value problem for hyperbolic systems. Communication of Pure and Applied Mathematics 1970; 23:277-298.
7. Fox L. Numerical Solution of Ordinary and Partial Differential Equations. Pergamon Press: New York, 1962.
8. Yee HC. Numerical approximation of boundary conditions with applications to inviscid equations of gas dynamics. NASA Technical Memorandum 81265, 1981.
9. Yee HC, Beam RM, Warming RF. Boundary approximations for implicit schemes for one-dimensional inviscid equations of gas dynamics. AJAA Journal 1982; 20(9):1203-1211.
10. Jin M, Fread DL. Dynamic flood routing with explicit and implicit numerical solution schemes. Journal of Hydraulic Engineering (ASCE) 1997; 123(3):166-173.
11. Villanueva I. Estudio de regímenes transitorios y permanentes en ríos y canales. Ph. D. Thesis, University of Zaragoza, 1999.
12. Burguete J, García Navarro P, Aliod R. Numerical simulation of runoff from extreme rainfall events in a mountain water catchment. Natural Hazards in Earth System Sciences 2002; 2:1-9.
13. Saint Venant AJCB de. Théory de mouvement non-permanent des eaux avec aplication aux crues de rivières et á l'introduction des marées dans leur lit. Comptes Rendus de l'Académie des Sciences, Paris, 1871.
14. Gauckler PG. Études théoriques et practiques sur l'écoulement et le mouvement des eaux. Comptes Rendus de l'Académie des Sciences, Paris, 1867.
15. Manning R. On the Flow of Water in Open Channels and Pipes. Institution of Civil Engineers of Ireland, 1890.
16. Hirsch C. Computational Methods for Inviscid and Viscous Flows: Numerical Computation of Internal and External Flows. Wiley: New York, 1990.
17. Roe PL. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics 1981; 43(2):357-372.
18. Sweby PK. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis 1984; 21:995-1011.
19. Roe PL. Generalized formulation of TVD Lax-Wendroff schemes. ICASE Report 84-53, NASA CR-172478, NASA Langley Research Center, 1984.
20. Courant R, Friedrichs KO, Lewy H. Über die partiellen Differenzengleichungen der mathematisches. Mathematische Annalen 1928; 100:32-74.
21. Gustafsson B. The convergence rate for difference approximations to mixed initial boundary value problem. Mathematics of Computations 1975; 29:396-406.
22. Kreiss HO. Difference approximations for mixed initial boundary value problems. Proceedings of the Royal Society of London Series A 1971; 323:255-261.
23. Gustafsson B, Kreiss HO, Sundström A. Stability theory of difference approximations for mixed initial boundary value problems. Mathematics of Computations 1972; 26:649-686.
24. MacDonald I. Analysis and computation of steady open channel flow. Ph.D. Thesis, University of Reading, 1996.
25. MacDonald I, Baines MJ, Nichols NK, Samuels PG. Analytical benchmark solutions for open-channel flows. Journal of Hydraulic Engineering (ASCE) 1997; 123(11):1041-1045.
26. Strickler A. Beiträge zur Frage der Geschwindigkeitsformel und der Rauhligkeitszahlen für Ströme, Kanäle und Geschlossene Leitungen. Mitt. des Eidgenössischen Amtes für Wasserwirtschaft: Bern, vol. 16, 1923.