Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow

Journal of Computational Physics

Volumn 228, Issue 15, 2009, Pages 5539-5573

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

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b CSIC   (Spain)

Author keywords

Coupled system; Multi component transport; Reactive source terms; Shallow flow; Solute constraints; Turbulence; Variable domain; Well balanced approach; s( ) lunate model

Indexed keywords

FLOW OF WATER; HYDRAULICS; NUMERICAL MODELS;

COUPLED SYSTEMS; MULTI-COMPONENT TRANSPORT; MULTICOMPONENTS; REACTIVE SOURCE TERM; REACTIVE SOURCES; SHALLOW FLOW; SOLUTE CONSTRAINT; SOURCE TERMS; VARIABLE DOMAIN; WELL BALANCED; WELL-BALANCED APPROACH; Κ S(-) Ε{LUNATE} MODEL;

FRICTION;

EID: 67349116002     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.04.039     Document Type: Article

References (31)

1. Batten P., Lambert C., and Causon D.M. Positively conservative high-resolution convection schemes for unstructured elements. Int. J. Numer. Method Eng. 39 (1996) 821-1838
2. Begnudelli L., and Sanders F. Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying. J. Hydraul. Eng. 132 (2006) 371-384
3. Benkhaldoun F., Elmahi I., and Seaïd M. Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes. J. Comput. Phys. 226 (2007) 180-203
4. Brufau P., Vázquez-Cendón M.E., and García-Navarro P. A numerical model for the flooding and drying of irregular domains. J. Numer. Method Fluid 39 (2002) 247-275
5. Burguete J., and García-Navarro P. Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows. Int. J. Numer. Method Fluid 37 (2001) 209-248
6. Burguete J., García-Navarro P., and Murillo J. Preserving bounded and conservative solutions of transport in one-dimensional shallow-water flow with upwind numerical schemes: application to fertigation and solute transport in rivers. Int. J. Numer. Method Fluid 56 (2008) 1731-1764
7. Cea L., Pena L., Puertas J., Vázquez-Cendón M.E., and Pea E. Application of several depth-averaged turbulence models to simulate flow in vertical slot fishways. J. Hydraul. Eng., ASCE 39 (2007) 133-160
8. Courant R., Isaacson E., and Rees M. On the solution of nonlinear hyperbolic differential equations by finite differences. Commun. Pure Appl. Math. 5 (1952) 243-255
9. Durbin P. On the κ-ε{lunate} stagnation point anomaly. Int. J. Heat Fluid Flow 17 (1996) 89-90
10. Fe J., Navarrina F., Puertas J., Vellando P., and Ruiz D. Experimental validation of two depth-averaged turbulence models. J. Numer. Method Fluid (2008) 10.1002/fld.1880
11. Godlewsky E., and Raviart P.A. Numerical Approximation of Hyperbolic Systems of Conservation Laws vol. 403 (1996), Springer-Verlag, New York
12. Goodman J.B., and LeVeque R.J. On the accuracy of stable schemes for 2D scalar conservation laws. Math. Comput. 45 (1985) 15-21
13. Hubbard M.E., and García-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys. 165 (2000) 89-125
14. Leveque R.J. Finite Volume Methods for Hyperbolic Problems (2002), Cambridge University Press, New York p. 380
15. Murillo J., Burguete J., Brufau P., and García-Navarro P. Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D. Int. J. Numer. Method Fluid 49 (2005) 267-299
16. Murillo J., García-Navarro P., Burguete J., and Brufau P. A conservative 2D model of inundation flow with solute transport over dry bed. Int. J. Numer. Method Fluid 52 (2006) 1059-1092
17. Murillo J., García-Navarro P., Burguete J., and Brufau P. The influence of source terms on stability accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes. Int. J. Numer. Method Fluid 54 (2007) 543-590
18. Murillo J., Burguete J., and García-Navarro P. Analysis of a second-order upwind method for the simulation of solute transport in 2D shallow water flow. Int. J. Numer. Method Fluid 56 (2008) 661-686
19. Murillo J., García-Navarro P., and Burguete J. Time step restrictions for well-balanced shallow water solutions in non-zero velocity steady states. Int. J. Numer. Method Fluid (2009) 10.1002/fld.1939
20. J. Qu, Three-dimensional turbulence modelling for free surface flows. Ph.D. Thesis, Concordia University, Montreal, Canada, 2005.
21. Rastogi A.K., and Rodi W. Predictions of heat and mass transfer in open channels. J. Hydraul. Div., ASCE (1978) 397-420
22. Roe P.L. A basis for upwind differencing of the two-dimensional unsteady Euler equations. Numerical Methods in Fluid Dynamics vol. II (1986), Oxford University Press, Oxford
23. Rosatti G., Murillo J., and Fraccarollo L. Generalized Roe schemes for 1D two-phase free-surface flows over a mobile bed. J. Comput. Phys. 54 (2007) 543-590
24. Rutherford J.C. River Mixing (1994), Wiley, New York p. 21
25. Soares-Frazao S., and Zech Y. Experimental study of dam-break flow against an isolated obstacle. J. Hydraul. Res. 45 (1994) 27-36
26. Thacker W.C. Some exact solutions to the nonlinear shallow water equations. J. Fluid Mech. 107 (1981) 499-508
27. Toro E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics (1997), Springer, Berlin p. 526
28. Toro E.F. Shock-Capturing Methods for Free-Surface Shallow Flows (2001), Wiley, New York p. 109
29. Vázquez-Cendón M.E. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys. 148 (1999) 497-498
30. Vázquez-Cendón M.E. Implicit and explicit upwind schemes for the 2D shallow water equations in unstructured meshes. Numer. Model. Hydrodynam. Syst., Zaragoza 1 (1999) 251-321
31. Wierse M. A new theoretically motivated higher order upwind scheme on unstructured grids of simplices. Adv. Comput. Math. 7 (1997) 303-335