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Volumn 25, Issue 6, 2004, Pages 2050-2065

A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows

Author keywords

Finite volume schemes; Shallow water equations; Well balanced schemes

Indexed keywords

FINITE VOLUME METHOD; GEOMETRY; NUMERICAL ANALYSIS; SURFACE TOPOGRAPHY; WAVES;

EID: 4644342716     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827503431090     Document Type: Article
Times cited : (911)

References (32)
  • 3
    • 0038746749 scopus 로고    scopus 로고
    • A wave propagation method for conservation laws and balance laws with spatially varying flux functions
    • D. S. BALE, R. J. LEVEQUE, S. MITRAN, AND J. A. ROSSMANITH, A wave propagation method for conservation laws and balance laws with spatially varying flux functions, SIAM J. Sci. Comput., 24 (2002), pp. 955-978.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 955-978
    • Bale, D.S.1    Leveque, R.J.2    Mitran, S.3    Rossmanith, J.A.4
  • 4
    • 0037234915 scopus 로고    scopus 로고
    • Equilibrium schemes for scalar conservation laws with stiff sources
    • R. BOTCHORISHVILI, B. PERTHAME, AND A. VASSEUR, Equilibrium schemes for scalar conservation laws with stiff sources, Math. Comp., 72 (2003), pp. 131-157.
    • (2003) Math. Comp. , vol.72 , pp. 131-157
    • Botchorishvili, R.1    Perthame, B.2    Vasseur, A.3
  • 5
    • 10244233725 scopus 로고    scopus 로고
    • Well-balanced finite volume methods for nearly hydrostatic flows
    • submitted. See also PIK-report 84, Potsdam Institute for Climate Impact Research, Potsdam, Germany
    • N. BOTTA, R. KLEIN, S. LANGENBERG, AND S. LÜTZENKIRCHEN, Well-balanced finite volume methods for nearly hydrostatic flows, J. Comput. Phys., submitted. (See also PIK-report 84, Potsdam Institute for Climate Impact Research, Potsdam, Germany, available online from http://www.pik-potsdam.de/reports.)
    • J. Comput. Phys.
    • Botta, N.1    Klein, R.2    Langenberg, S.3    Lützenkirchen, S.4
  • 6
    • 10244270313 scopus 로고    scopus 로고
    • Distinguished limits, multiple scales asymptotics, and numerics for atmospheric flows
    • Breckenridge, CO, American Meteorological Society, Boston, MA
    • N. BOTTA, R. KLEIN, AND A. OWINOH, Distinguished limits, multiple scales asymptotics, and numerics for atmospheric flows, in Proceedings of the 13th International Conference on Atmosphere-Ocean Fluid Dynamics, Breckenridge, CO, American Meteorological Society, Boston, MA, 2001.
    • (2001) Proceedings of the 13th International Conference on Atmosphere-ocean Fluid Dynamics
    • Botta, N.1    Klein, R.2    Owinoh, A.3
  • 7
    • 10244241405 scopus 로고    scopus 로고
    • Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources
    • Birkhäuser
    • F. BOUCHOT, Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws, and Well-Balanced Schemes for Sources, Frontiers in Math., Birkhäuser, 2004.
    • (2004) Frontiers in Math.
    • Bouchot, F.1
  • 8
    • 10244238538 scopus 로고    scopus 로고
    • Frontal geostrophic adjustment and nonlinearwave phenomena in one dimensional rotating shallow water. Part 2: High resolution numerical investigation
    • to appear
    • F. BOUCHUT, J. LESOMMER, AND V. ZEITLIN, Frontal geostrophic adjustment and nonlinearwave phenomena in one dimensional rotating shallow water. Part 2: High resolution numerical investigation, J. Fluid Mech., to appear.
    • J. Fluid Mech.
    • Bouchut, F.1    Lesommer, J.2    Zeitlin, V.3
  • 11
    • 0037404907 scopus 로고    scopus 로고
    • Some approximate Godunov schemes to compute shallow-water equations with topography
    • T. GALLOUËT, J.-M. HÉRARD, AND N. SEGUIN, Some approximate Godunov schemes to compute shallow-water equations with topography, Computers and Fluids, 32 (2003), pp. 479-513.
    • (2003) Computers and Fluids , vol.32 , pp. 479-513
    • Gallouët, T.1    Hérard, J.-M.2    Seguin, N.3
  • 12
    • 85114329546 scopus 로고    scopus 로고
    • Numerical approximation of hyperbolic systems of conservation laws
    • Springer-Verlag, New York
    • E. GODLEWSKI AND P.-A. RAVIART, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Appl. Math. Sci. 118, Springer-Verlag, New York, 1996.
    • (1996) Appl. Math. Sci. , vol.118
    • Godlewski, E.1    Raviart, P.-A.2
  • 13
    • 0034209981 scopus 로고    scopus 로고
    • A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
    • L. GOSSE, A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms, Comput. Math. Appl., 39 (2000), pp. 135-159.
    • (2000) Comput. Math. Appl. , vol.39 , pp. 135-159
    • Gosse, L.1
  • 14
    • 0000711631 scopus 로고    scopus 로고
    • A well-balanced scheme designed for inhomogeneous scalar conservation laws
    • L. GOSSE AND A.-Y. LEROUX, A well-balanced scheme designed for inhomogeneous scalar conservation laws, C. R. Acad. Sci. Paris Sér. I Math., 323 (1996), pp. 543-546.
    • (1996) C. R. Acad. Sci. Paris Sér. I Math. , vol.323 , pp. 543-546
    • Gosse, L.1    Leroux, A.-Y.2
  • 15
    • 79955716290 scopus 로고    scopus 로고
    • Proceedings of the second workshop on dam-break wave simulation
    • Châtou, France
    • N. GOUTAL AND F. MAUREL, Proceedings of the Second Workshop on Dam-Break Wave Simulation, Technical report EDF/DER HE-43/97/016/B, Châtou, France, 1997.
    • (1997) Technical Report , vol.EDF-DER HE-43-97-016-B
    • Goutal, N.1    Maurel, F.2
  • 16
    • 1542576141 scopus 로고    scopus 로고
    • A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
    • J. M. GREENBERG AND A.-Y. LEROUX, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations, SIAM J. Numer. Anal., 33 (1996), pp. 1-16.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1-16
    • Greenberg, J.M.1    Leroux, A.-Y.2
  • 17
    • 0029323645 scopus 로고
    • Convergence of the 2 × 2 Godunov method for a general resonant nonlinear balance law
    • E. ISAACSON AND B. TEMPLE, Convergence of the 2 × 2 Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math., 55 (1995), pp. 625-640.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 625-640
    • Isaacson, E.1    Temple, B.2
  • 18
    • 0035537697 scopus 로고    scopus 로고
    • A steady-state capturing method for hyperbolic systems with geometrical source terms
    • S. JIN, A steady-state capturing method for hyperbolic systems with geometrical source terms, Math. Model. Numer. Anal., 35 (2001), pp. 631-645.
    • (2001) Math. Model. Numer. Anal. , vol.35 , pp. 631-645
    • Jin, S.1
  • 21
    • 10244228763 scopus 로고    scopus 로고
    • Riemann solvers for some hyperbolic problems with a source term
    • Actes du 30̀me Congrès d'Analyse Numérique: CANum '98 (Arles, 1998)
    • A.-Y. LEROUX, Riemann solvers for some hyperbolic problems with a source term, in Actes du 30̀me Congrès d'Analyse Numérique: CANum '98 (Arles, 1998), ESAIM Proc. 6, Soc. Math. Appl. Indust., Paris, 1999, pp. 75-90.
    • (1999) ESAIM Proc. 6, Soc. Math. Appl. Indust., Paris , vol.6 , pp. 75-90
    • Leroux, A.-Y.1
  • 22
    • 84884956721 scopus 로고    scopus 로고
    • Discrétisation des termes sources raides dans les problèmes hyperboliques
    • Ecoles CEAEDF-INRIA "problèmes non linéaires appliqués," INRIA Rocquencourt, Le Chesnay, France
    • A.-Y. LEROUX, Discrétisation des termes sources raides dans les problèmes hyperboliques, in Systèmes hyperboliques: Nouveaux schémas et nouvelles applications. Ecoles CEAEDF-INRIA "problèmes non linéaires appliqués," INRIA Rocquencourt, Le Chesnay, France, 1998; available online from http://www-gm3.univ-mrs.fr/~leroux/publications/ ay.le_roux.html.
    • (1998) Systèmes Hyperboliques: Nouveaux Schémas et Nouvelles Applications
    • Leroux, A.-Y.1
  • 24
    • 0001315315 scopus 로고    scopus 로고
    • Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
    • 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. 346365.
    • (1998) J. Comput. Phys. , vol.146 , pp. 346365
    • Leveque, R.J.1
  • 25
    • 0001682883 scopus 로고
    • Nonlinear resonance for quasilinear hyperbolic equation
    • T.-P. LIU, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys., 28 (1987), pp. 2593-2602.
    • (1987) J. Math. Phys. , vol.28 , pp. 2593-2602
    • Liu, T.-P.1
  • 28
    • 0012588539 scopus 로고    scopus 로고
    • A kinetic scheme for the Saint-Venant system with a source term
    • B. PERTHAME AND C. SIMEONI, A kinetic scheme for the Saint-Venant system with a source term, Calcolo, 38 (2001), pp. 201-231.
    • (2001) Calcolo , vol.38 , pp. 201-231
    • Perthame, B.1    Simeoni, C.2
  • 29
    • 0742302514 scopus 로고    scopus 로고
    • Convergence of the upwind Interface source method for hyperbolic conservation laws
    • T. Hou and E. Tadmor, eds., SpringerVerlag, Berlin
    • B. PERTHAME AND C. SIMEONI, Convergence of the upwind Interface source method for hyperbolic conservation laws, in Proceedings of Hyp2002, T. Hou and E. Tadmor, eds., SpringerVerlag, Berlin, 2003.
    • (2003) Proceedings of Hyp2002
    • Perthame, B.1    Simeoni, C.2
  • 30
    • 84889809594 scopus 로고    scopus 로고
    • Riemann solvers and numerical methods for fluid dynamics
    • Springer-Verlag, Berlin
    • E. F. TORO, Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction, 2nd ed., Springer-Verlag, Berlin, 1999.
    • (1999) A Practical Introduction, 2nd Ed.
    • Toro, E.F.1
  • 31
    • 0348194970 scopus 로고    scopus 로고
    • Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
    • M. E. VAZQUEZ-CENDON, Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry, J. Comput. Phys., 148 (1999), pp. 497-526.
    • (1999) J. Comput. Phys. , vol.148 , pp. 497-526
    • Vazquez-Cendon, M.E.1
  • 32
    • 0037141036 scopus 로고    scopus 로고
    • Well-balanced gas-kinetic scheme for the shallow water equations with source terms
    • K. XU, well-balanced gas-kinetic scheme for the shallow water equations with source terms, J. Comput. Phys., 178 (2002), pp. 533-562.
    • (2002) J. Comput. Phys. , vol.178 , pp. 533-562
    • Xu, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.