Analysis of a second-order upwind method for the simulation of solute transport in 2D shallow water flow

International Journal for Numerical Methods in Fluids

Volumn 56, Issue 6, 2008, Pages 661-686

  Murillo, J ^a   García Navarro, Pigar ^a   Burguete, J ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b CSIC   (Spain)

Author keywords

Conservation; Convection; Coupled system; Diffusion; Finite volumes; Shallow water flow; Solute transport; Source terms; Two dimensional model

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; DIFFUSION; FINITE VOLUME METHOD; SOLUTE TRANSPORT; TWO DIMENSIONAL;

FIRST-ORDER UPWIND TECHNIQUE; SHALLOW WATER FLOW;

FLOW OF WATER;

COMPUTATIONAL FLUID DYNAMICS; DIFFUSION; FINITE VOLUME METHOD; FLOW OF WATER; SOLUTE TRANSPORT; TWO DIMENSIONAL;

EID: 39549095826     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1546     Document Type: Article

References (26)

1. Rutherford JC. River Mixing. Wiley: New York, 1994.
2. Murillo J, Burguete J, Brufau P, García-Navarro P. Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D. International Journal for Numerical Methods in Fluids 2005; 49:267-299.
3. Néelz S, Wallis SG. Taking accuracy of a semi-Lagrangian method for advection-dispersion modelling in rivers. International Journal for Numerical Methods in Fluids 2006; 53(1):1-21.
4. Nair RD, Scroggs JS, Semazzi FHM. A forward-trajectory global semi-Lagrangian transport scheme. Journal of Computational Physics 2003; 190(1):275-294.
5. Oliveira A, Fortunato AB. Toward an oscillation-free, mass conservative, Eulerian-Lagrangian transport model. Journal of Computational Physics 2002; 183:142-164.
6. Begnudelli L, Sanders F. Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying. Journal of Hydraulic Engineering 2006; 132(4):371-384.
7. Courant R, Isaacson E, Rees M. On the solution of nonlinear hyperbolic differential equations by finite differences. Communications on Pure and Applied Mathematics 1952; 5:243-255.
8. Murillo J, García-Navarro P, Brufau P, Burguete J. Extension of an explicit finite volume method to large time steps (CFL> 1): application to shallow water flows. International Journal for Numerical Methods in Fluids 2005; 50:63-102.
9. Murillo J, García-Navarro P, Burguete J, Brufau P. A conservative 2d model of inundation flow with solute transport over dry bed. International Journal for Numerical Methods in Fluids 2006; 52(10):1059-1092.
10. Murillo J, García-Navarro P, Burguete J. The influence of source terms on stability, accuracy and conservation in 2d shallow flow simulation using triangular finite volumes. International Journal for Numerical Methods in Fluids 2007; 54(5):543-590.
11. Benqué JP, Hauguel A, Violet PL. Engineering Applications of Computational Hydraulics, vol. II. Pitman: London, 1982.
12. Vreugdenhil CB. Numerical Methods for Shallow-Water Flow. Kluwer Academic Publishers: Dordrecht, 1994.
13. Brufau P, Vázquez-Cendón ME, García-Navarro P. A numerical model for the flooding and drying of irregular domains. International Journal for Numerical Methods in Fluids 2002; 39:247-275.
14. Cunge JA, Holly FM, Verwey A. Practical Aspects of Computational River Hydraulics. Pitman: London, 1980.
15. Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43(2):357-372.
16. García-Navarro P, Vázquez-Cendón ME. On numerical treatment of the source terms in the shallow water equations. Computers and Fluids 2000; 29:951-979.
17. Hubbard ME, García-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. Journal of Computational Physics 2000; 165:89-125.
18. Van Leer B. On the relation between the upwind-differencing schemes of Godunov, Enguist-Osher and Roe. SIAM Journal on Scientific and Statistical Computing 1985; 5(1):1-20.
19. Batten P, Lambert C, Causon DM. Positively conservative high-resolution convection schemes for unstructured elements. International Journal for Numerical Methods in Engineering 1996; 39:1821-1838.
20. Wierse M. A new theoretically motivated higher order upwind scheme on unstructured grids of simplices. Advances in Computational Mathematics 1997; 7:303-335.
21. Leveque RJ. Numerical Methods for Conservation Laws. Birkhäuser: Basel, 1990.
22. Fischer HB, Imberger J, List EJ, Koh RCY, Brooks NH. Mixing in Inland and Coastal Waters. Academic Press: Orlando, U.S.A., 1979.
23. Stoker JJ. Water Waves. Interscience: New York, 1957.
24. Toro EF. Shock-Capturing Methods for Free-Surface Shallow Flows. Wiley: New York, 2001.
25. Thacker WC. Some exact solutions to the non linear shallow water equations. Journal of Fluid Mechanics 1981; 107:499-509.
26. Méndez PL, Brufau P, Puertas J. An experimental approach to the dam break problem. Real data to check numerical models. XXIX IAHR Congress, Beijing, China, 2001.