Implicit schemes with large time step for non-linear equations: Application to river flow hydraulics

International Journal for Numerical Methods in Fluids

Volumn 46, Issue 6, 2004, Pages 607-636

  Burguete, J ^a   Garcia Navarro P ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

High CFL number; Implicit schemes; Non linear equations; Shallow water; Unsteady flow with shocks; Upwind discretization

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; FLOOD CONTROL; HYDRAULICS; MATHEMATICAL MODELS; RIVERS; ROBUSTNESS (CONTROL SYSTEMS);

BIDIAGONAL SCHEMES; TRANSCRITICAL FLOWS; UPWIND IMPLICIT SCHEMES;

NONLINEAR EQUATIONS;

FLOOD ROUTING; MATHEMATICAL ANALYSIS; OPEN CHANNEL FLOW; RIVER CHANNEL; SHALLOW WATER; UNSTEADY FLOW;

EID: 4944267766     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.772     Document Type: Article

References (22)

1. Preissmann A. Propagation des intumescences dans les cannaux et rivières. First Congress of the French Association for Computation AFCAL, Grenoble, 1961; 443-442.
2. Abbott MB, Ionescu F. On the numerical computation of nearly horizontal flows. Journal of Hydraulic Research 1967; 5(2):97-117.
3. Beam RM, Warming RF. An implicit factored scheme for the compressible Navier-Stokes equations. AIAA Journal 1978; 16:393-402.
4. MacCormack RW. A numerical method for solving the equations of compressible viscous flow. AIAA Journal 1982; 20:1275-1281.
5. Casier F, Deconinck H, Hirsch C. A class of bidiagonal schemes for solving Euler equations. AIAA Journal 1983; 22:1556-1563.
6. Meselhe EA, Sotiropoulos F, Holly Jr FM. Numerical simulation of transcritical flow in open channels. Journal of Hydraulic Engineering 1997; 123(9):774-782.
7. Yee HC. Construction of explicit and implicit symmetric TVD schemes and their applications. Journal of Computational Physics 1987; 68:151-179.
8. Cunge JA, Holly FM, Verwey A. Practical Aspects of Computational River Hydraulics. Pitman: London, U.K., 1980.
9. Hirsch C. Computational Methods for Inviscid and Viscous Flows: Numerical Computation of Internal and External Flows. Wiley: New York, 1990.
10. Burguete J, Garcia 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.
11. Glaister P. Approximate Riemann solutions of the shallow water equations. Journal of Hydraulic Research 1988; 26:293-306.
12. Bermúdez A, Vázquez Cendón ME. Upwind methods for hyperbolic conservation laws with source terms. Computers and Fluids 1994; 23(8):1049-1071.
13. 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.
14. Roe PL. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics 1981; 43(2):357-372.
15. Harten A, Hyman JM. Self adjusting grid methods for one-dimensional hyperbolic conservation laws. Journal of Computational Physics 1983; 50:235-269.
16. Yee HC, Beam RM, Warming RF. Boundary approximations for implicit schemes for one-dimensional inviscid equations of gasdynamics. AIAA Journal 1982; 20(9):1203-1211.
17. Burguete J, García Navarro P, Aliod R. Numerical simulation of runoff from extreme rainfall events in a mountain water cachtment. Natural Hazards in Earth System Sciences 2002; 2:1-9.
18. Burguete J. Modelos unidimensionales de flujos de superficie libre y transporte en geometrías irregulares: Aplicación al flujo en ríos. Ph.D. Thesis, University of Zaragoza.
19. Burgers JM. A mathematical model illustrating the theory of turbulence. Advances in Applied Mechanics 1948; 1:171-199.
20. Stoker JJ. Water Waves. Interscience Publishers: New York, 1957.
21. MacDonald I, Baines MJ, Nichols NK, Samuels PG. Analytical benchmark solutions for open-channel flows. ASCE Journal of Hydraulic Engineering 1997; 123(11):1041-1045.
22. MacDonald I. Analysis and computation of steady open channel flow. Ph.D. Thesis, University of Reading, 1996.