Balanced central schemes for the shallow water equations on unstructured grids

SIAM Journal on Scientific Computing

Volumn 27, Issue 2, 2006, Pages 532-552

  Bryson, Steve ^a,b   Levy, Doron ^c  

^a Stanford University   (United States)

^b NASA AMES RESEARCH CENTER   (United States)

^c STANFORD UNIVERSITY   (United States)

Author keywords

Balance laws; Central schemes; Shallow water equations; Unstructured grids

Indexed keywords

COMPUTER SIMULATION; TOPOLOGY; TRIANGULATION;

BALANCE LAWS; CENTRAL SCHEMES; SHALLOW WATER EQUATIONS; UNSTRUCTURED GRIDS;

APPROXIMATION THEORY;

EID: 33644941748     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040605539     Document Type: Article

References (27)

1. P. ARMINJON AND M.-C. VIALLON, Généralisation du schéma de Nessyahu-Tadmor pour une équation hyperbolique à deux dimensions d'espace, C. R. Acad. Sci. Paris Sér. I Math., 320 (1995), pp. 85-88.
2. P. ARMINJON, M.-C. VIALLON, AND A. MADRANE, A finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for conservation laws on unstructured grids, Int. J. Comput. Fluid Dyn., 9 (1997), pp. 1-22.
3. E. AUDUSSE AND M.-O. BRISTEAU, Transport of pollutant in shallow water: A two time steps kinetic method, M2AN Math. Model. Numer. Anal., 37 (2003), pp. 389-416.
4. E. AUDUSSE, M.-O. BRISTEAU, AND B. PERTHAME, Kinetic Schemes for Saint-Venant Equations with Source Terms on Unstructured Grids, INRIA report RR-3989, 2000.
5. R. BOTCHORISHVILI, B. PERTHAME, AND A. VASSEUR, Equilibrium schemes for scalar conservation laws with stiff sources, Math. Comp., 72 (2003), pp. 131-157.
6. R. BOTCHORISHVILI AND O. PIRONNEAU, Finite volume schemes with equilibrium-type dis-cretization of source terms for scalar conservation laws, J. Comput. Phys., 187 (2003), pp. 391-427.
7. A. I. DELIS AND TH. KATSAOUNIS, Relaxation schemes for the shallow water equations, Internat. J. Numer. Methods Fluids, 41 (2003), pp. 695-719.
8. K. O. FRIEDRICHS AND P. D. LAX, Systems of conservation equations with a convex extension, Proc. Natl. Acad. Sci. USA, 68 (1971), pp. 1686-1688.
9. T. GALLOUËT, J.-M. HÉRARD, AND N. SEGUIN, Some approximate Godunov schemes to compute shallow-water equations with topography, Comput. & Fluids., 32 (2003), pp. 479-513.
10. J. F. GERBEAU AND B. PERTHAME, Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation, Discrete Contin. Dyn. Syst. Ser. B, 1 (2001), pp. 89-102.
11. L. GOSSE, A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms, Math. Models Methods Appl. Sci., 11 (2001), pp. 339-365.
12. M. E. HUBBARD, On the accuracy of one-dimensional models of steady converging/diverging open channel flows, Internat. J. Numer. Methods Fluids, 35 (2001), pp. 785-808.
13. G.-S. JIANG AND E. TADMOR, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput., 19 (1998), pp. 1892-1917.
14. A. KURGANOV AND D. LEVY, Central-upwind schemes for the Saint-Venant system, M2AN Math. Model. Numer. Anal., 36 (2002), pp. 397-425.
15. A. KURGANOV, S. NOELLE, AND G. PETROVA, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput., 23 (2001), pp. 707-740.
16. A. KURGANOV AND G. PETROVA, Central-upwind schemes on triangular grids for hyperbolic systems of conservation laws, Numer. Methods Partial Differential Equations, 21 (2005), pp. 536-552.
17. A. KURGANOV AND E. TADMOR, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160 (2000), pp. 214-282.
18. R. J. LEVEQUE, Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm, J. Comput. Phys., 146 (1998), pp. 346-365.
19. R. J. LEVEQUE AND D. S. BALE, Wave propagation methods for conservation laws with source terms, in Hyperbolic Problems: Theory, Numerics, Applications, Vol. II (Zürich, 1998),
20. Internat. Ser. Numer. Math. 130, Birkhäuser, Basel, 1999, pp. 609-618.
21. S. F. LIOTTA, V. ROMANO, AND G. RUSSO, Central schemes for systems of balance laws, in Hyperbolic Problems: Theory, Numerics, Applications, Vol. II (Zürich, 1998),
22. Internat. Ser. Numer. Math. 130, Birkhäuser, Basel, 1999, pp. 651-660.
23. H. NESSYAHU AND E. TADMOR, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
24. B. PERTHAME AND C. SIMEONI, A kinetic scheme for the Saint-Venant system with a source term, Calcolo, 38 (2001), pp. 201-231.
25. G. Russo, Central schemes for balance laws, in Hyperbolic Problems: Theory, Numerics, Applications, Vol. I, II (Magdeburg, 2000),
26. Internat. Ser. Numer. Math. 140, 141, Birkhäuser, Basel, 2001, pp. 821-829.
27. A. J. C. DE SAINT-VENANT, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivière at à l'introduction des marées dans leur lit, C. R. Acad. Sci. Paris, 73 (1871), pp. 147-154.