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Volumn 234, Issue 1, 2010, Pages 58-72

A simple finite volume method for the shallow water equations

Author keywords

Dam break problems; Finite volume scheme; Method of characteristics; Shallow water equations

Indexed keywords

ANALYTICAL SOLUTIONS; BENCHMARK TESTS; CONSERVATION EQUATIONS; DAM-BREAK PROBLEMS; FINITE VOLUME SCHEMES; METHOD OF CHARACTERISTICS; NUMERICAL FLUX; NUMERICAL SOLUTION; RIEMANN PROBLEM; SHALLOW WATER EQUATIONS; TIME INTEGRATION;

EID: 77649178663     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.12.005     Document Type: Article
Times cited : (49)

References (21)
  • 1
    • 0003933895 scopus 로고
    • Interscience Publishers, Inc., New York
    • Stoker J.J. Water Waves (1986), Interscience Publishers, Inc., New York
    • (1986) Water Waves
    • Stoker, J.J.1
  • 3
    • 0027561554 scopus 로고
    • A high resolution Godunov-type scheme in finite volumes for the 2D shallow water equations
    • Alcrudo F., and Navarro P.G. A high resolution Godunov-type scheme in finite volumes for the 2D shallow water equations. Internat. J. Numer. Methods Fluids 16 (1993) 489-505
    • (1993) Internat. J. Numer. Methods Fluids , vol.16 , pp. 489-505
    • Alcrudo, F.1    Navarro, P.G.2
  • 4
    • 0037404907 scopus 로고    scopus 로고
    • Some approximate Godunov schemes to compute shallow water equations with topography
    • Gallouët T., Herard J.M., and Seguin N. Some approximate Godunov schemes to compute shallow water equations with topography. Comput. & Fluids 32 (2003) 479-513
    • (2003) Comput. & Fluids , vol.32 , pp. 479-513
    • Gallouët, T.1    Herard, J.M.2    Seguin, N.3
  • 5
    • 0001315315 scopus 로고    scopus 로고
    • Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
    • LeVeque Randall J. Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm. J. Comput. Phys. 146 (1998) 346-365
    • (1998) J. Comput. Phys. , vol.146 , pp. 346-365
    • LeVeque Randall, J.1
  • 7
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors and difference schemes
    • Roe P.L. Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys. 43 (1981) 357-372
    • (1981) J. Comput. Phys. , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 8
    • 0028534347 scopus 로고
    • Upwind methods for hyperbolic conservation laws with source terms
    • Bermudez A., and Vázquez-Cendón M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. & Fluids 23 (1994) 1049-1071
    • (1994) Comput. & Fluids , vol.23 , pp. 1049-1071
    • Bermudez, A.1    Vázquez-Cendón, M.E.2
  • 9
    • 0348194970 scopus 로고    scopus 로고
    • Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
    • Vázquez 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) 497-526
    • (1999) J. Comput. Phys. , vol.148 , pp. 497-526
    • Vázquez, M.E.1
  • 10
    • 0033838423 scopus 로고    scopus 로고
    • On numerical treatment of the source terms in the shallow water equations
    • Garcia-Navarro P., and Vazquez-Cendon M.E. On numerical treatment of the source terms in the shallow water equations. Comput. & Fluids 29 (2000) 951-979
    • (2000) Comput. & Fluids , vol.29 , pp. 951-979
    • Garcia-Navarro, P.1    Vazquez-Cendon, M.E.2
  • 11
    • 0011032642 scopus 로고    scopus 로고
    • Flux difference splitting and the balancing of source terms and flux gradients
    • Hubbard M.E., and Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys. 165 (2000) 89-125
    • (2000) J. Comput. Phys. , vol.165 , pp. 89-125
    • Hubbard, M.E.1    Garcia-Navarro, P.2
  • 12
    • 0035399783 scopus 로고    scopus 로고
    • Exact solutions to the Riemann problem of the shallow water equations with a bottom step
    • Alcrudo F., and Benkhaldoun F. Exact solutions to the Riemann problem of the shallow water equations with a bottom step. Comput. & Fluids 30 (2001) 643-671
    • (2001) Comput. & Fluids , vol.30 , pp. 643-671
    • Alcrudo, F.1    Benkhaldoun, F.2
  • 13
    • 4644342716 scopus 로고    scopus 로고
    • A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows
    • Audusse E., Bouchut F., Bristeau M.O., Klein R., and Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050-2065
    • (2004) SIAM J. Sci. Comput. , vol.25 , pp. 2050-2065
    • Audusse, E.1    Bouchut, F.2    Bristeau, M.O.3    Klein, R.4    Perthame, B.5
  • 14
    • 0036647452 scopus 로고    scopus 로고
    • ENO and WENO schemes with the exact conservation property for one-dimensional shallow-water equations
    • Vukovic S., and Sopta L. ENO and WENO schemes with the exact conservation property for one-dimensional shallow-water equations. J. Comput. Phys. 179 (2002) 593-621
    • (2002) J. Comput. Phys. , vol.179 , pp. 593-621
    • Vukovic, S.1    Sopta, L.2
  • 15
    • 33644933296 scopus 로고    scopus 로고
    • High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
    • Xing Y., and Shu C. High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. J. Comput. Phys. 214 (2006) 567-598
    • (2006) J. Comput. Phys. , vol.214 , pp. 567-598
    • Xing, Y.1    Shu, C.2
  • 16
    • 62849093327 scopus 로고    scopus 로고
    • Comparison of unstructured, staggered grid methods for the shallow water equations
    • Walters R.A., Hanert E., Pietrzak J., and Le Roux D.Y. Comparison of unstructured, staggered grid methods for the shallow water equations. Ocean Model. 28 (2009) 106-117
    • (2009) Ocean Model. , vol.28 , pp. 106-117
    • Walters, R.A.1    Hanert, E.2    Pietrzak, J.3    Le Roux, D.Y.4
  • 17
    • 5044227412 scopus 로고    scopus 로고
    • Non-oscillatory relaxation methods for the shallow water equations in one and two space dimensions
    • Seaïd M. Non-oscillatory relaxation methods for the shallow water equations in one and two space dimensions. Internat. J. Numer. Methods Fluids 46 (2004) 457-484
    • (2004) Internat. J. Numer. Methods Fluids , vol.46 , pp. 457-484
    • Seaïd, M.1
  • 19
    • 34548774022 scopus 로고    scopus 로고
    • A sign matrix based scheme for quasi-hyperbolic non-homogeneous PDEs with an analysis of the convergence stagnation problem
    • Sahmim S., Benkhaldoun F., and Alcrudo F. A sign matrix based scheme for quasi-hyperbolic non-homogeneous PDEs with an analysis of the convergence stagnation problem. J. Comput. Phys. 226 (2007) 1753-1783
    • (2007) J. Comput. Phys. , vol.226 , pp. 1753-1783
    • Sahmim, S.1    Benkhaldoun, F.2    Alcrudo, F.3
  • 20
    • 0023470250 scopus 로고
    • An efficient two-time-level semi-Lagrangian semi-implicit integration scheme
    • Temperton C., and Staniforth A. An efficient two-time-level semi-Lagrangian semi-implicit integration scheme. Q. J. R. Meteorol. Soc. 113 (1987) 1025-1039
    • (1987) Q. J. R. Meteorol. Soc. , vol.113 , pp. 1025-1039
    • Temperton, C.1    Staniforth, A.2
  • 21
    • 0000383020 scopus 로고
    • Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of advection-diffusion equation
    • Pudykiewicz J., and Staniforth A. Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of advection-diffusion equation. Atmos.-Ocean 22 (1984) 283-308
    • (1984) Atmos.-Ocean , vol.22 , pp. 283-308
    • Pudykiewicz, J.1    Staniforth, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.