Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique

Journal of Computational Physics

Volumn 186, Issue 2, 2003, Pages 503-526

  Brufau, P ^a   Garcia Navarro P ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Multidimensional upwind; Shallow water; Source terms; Unsteady flow

Indexed keywords

EQUATIONS OF MOTION; TOPOGRAPHY;

COMPLEX TOPOGRAPHIES; ELEMENT VOLUME; FINITE VOLUME APPROXIMATION; FREE SURFACE PROBLEMS; FREE-SURFACE FLOW; MULTIDIMENSIONAL UPWIND; NUMERICAL TECHNIQUES; SHALLOW WATERS; SOURCE TERMS; UP-WIND SCHEME;

NUMERICAL METHODS;

EID: 0344950457     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00072-X     Document Type: Article

References (34)

1. A. Bento Franco, Modelacao computacional e experimental de escoamentos provocados por roturas de barragens, Ph.D. Thesis, Univ. Técnica de Lisboa, 1996.
2. W. Betcheler, H. Kulisch, M. Nujic, 2-D dam-break flooding waves comparison between experimental and calculated results, Int. Rep. Inst. of Hydromech and Hyd., Univ. of the Federal Armed Forces, Munich, 1999.
3. P. Brufau, P. García-Navarro, M.E. Vázquez-Cendón, A numerical model for the flooding and drying of irregular domains, Int. J. Numer. Meth. Fluids 39 (2002) 247-275.
4. V.T. Chow, Open Channel Hydraulics, MacGraw-Hill, New York, 1959.
5. S.F. Davis, A rotationally biased upwind difference scheme for the Euler equations, J. Comp. Phys. 56 (1984).
6. H. Deconinck, C. Hirsch, J. Peuteman, Characteristics decomposition methods for the multidimensional Euler equations, in: 10th Int. Conf. in Num. Met. in Fluid Dyn., 1986, pp. 216-221.
7. H. Deconinck, R. Struijs, P.L. Roe, Fluctuation splitting for multidimensional convection problem: an alternative to finite volume and finite element methods, in: VKI Lecture series, 1990-03.
8. H. Deconinck, Analysis of wave propagation properties for the Euler equations in two-space dimensions, in: VKI Lecture series, 1994-05.
9. H. Deconinck, R. Struijs, G. Bourgois, P.L. Roe, High resolution shock capturing cell vertex advection schemes for unstructured grids, in: VKI Lecture series, 1994-05.
10. H. Deconinck, B. Koren (Eds.), Euler and Navier-Stokes solvers using multidimensional upwind schemes and multigrid acceleration, Notes on Numerical Fluid Mechanics, vol. 57, Vieweg, 1997.
11. P. García-Navarro, M.E. Hubbard, A. Priestley, Genuinely multidimensional upwinding for the 2D shallow water equations, J. Comp. Phys. 121 (1) (1995) 79-93.
12. P. García-Navarro, M.E. Vázquez-Cendón, On numerical treatment of the source terms in the shallow water equations, Comput. Fluids 29 (2000) 951-979.
13. P. García-Navarro, M.E. Hubbard, P. Brufau, Multidimensional upwind schemes: application to hydraulics, in: Godunov Methods: Theory and Applications, Kluwer Academic Press, 2000.
14. M. Heniche, Y. Secretan, P. Boudreau, M. Leclerc, A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries, Adv. Water Res. 23 (2000) 359-372.
15. M.E. Hubbard, Multidimensional upwinding and grid adaptation for conservation laws, Ph.D. Thesis, Univ. of Reading, England, 1996.
16. M.E. Hubbard, M.J. Baines, Conservative multidimensional upwinding for the steady two-dimensional shallow water equations, J. Comp. Phys. 138 (2) (1997) 419-448.
17. M.E. Hubbard, P.L. Roe, Compact high-resolution algorithms for time dependent advection on unstructured grids, Int. J. Numer. Methods Fluids (2000).
18. M.E. Hubbard, P. García-Navarro, Flux difference splitting and the balancing of source terms and flux gradients, J. Comp. Phys. 165 (1) (2000) 89-125.
19. M. Kawahara, T. Umetsu, Finite element method for moving boundary problems in river flow, Int. J. Numer. Methods Fluids 6 (1986) 365-386.
20. A.A. Khan, Modelling flow over an initially dry bed, J. Hyd. Res. 38 (5) (2000) 383-389.
21. R.J. LeVeque, Numerical Methods for Conservation Laws, 2nd ed., Birkhäuser, Basel, 1992.
22. D. Levy, K.G. Powell, B. Van Leer, Implementation of a grid-independent upwind scheme for the Euler equations, AIAA, 91-0635, 1991.
23. J. Marz, Improving time accuracy for residual distribution schemes, in: VKI Lecture notes, 1996-17.
24. H. Paillere, H. Deconinck, E. Van der Weide, Upwind residual distribution methods for compressible flow: an alternative to finite volume and finite element methods, in: VKI Lecture notes, 1997-02.
25. I.M. Parpia, D.J. Michalek, Grid-independent upwind scheme for multidimensional flow, AIAA J. 31 (4) (1993) 646-651.
26. P.L. Roe, Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics, J. Comp. Phys. 63 (1986) 458-476.
27. P.L. Roe, A basis for upwind differencing of the two-dimensional unsteady Euler equations, Numer. Methods Fluid Dyn. II (1986) 55-80.
28. P.L. Roe, R. Struijs, H. Deconinck, A conservative linearisation of the multidimensional Euler equations, J. Comp. Phys. (1993).
29. M.A. Rudgyard, Multidimensional wave decompositions for the Euler equations, in: VKI Lecture notes, 1993.
30. C.L. Rumsey, B. Van Leer, P.L. Roe, A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations, AIAA (1991) 91-1530.
31. P.A. Sleigh, M. Berzins, P.H. Gaskell, N.G. Wright, An unstructured finite volume algorithm for predicting flow in rivers and stuaries, Comput. & Fluids (1997).
32. Y. Tamura, K. Fujii, A multidimensional upwind scheme for the Euler equations on unstructured grids, in: 4th ISCFD Conference, 1991.
33. E. Van der Weide, Compressible flow simulation on unstructured grids using multi-dimensional upwind schemes, Ph.D. Thesis, Univ. of Delft, The Netherlands, 1998.
34. M.E. Vázquez-Cendón, Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry, J. Comp. Phys. 148 (1999) 497-526.