메뉴 건너뛰기




Volumn 5, Issue 4, 2007, Pages 865-885

The Riemann problem for the shallow water equations with discontinuous topography

Author keywords

Conservation law; Discontinuous topography; Riemann problem; Shallow water

Indexed keywords


EID: 39049136555     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2007.v5.n4.a7     Document Type: Article
Times cited : (115)

References (22)
  • 1
    • 0035399783 scopus 로고    scopus 로고
    • Exact solutions to the Riemann problem of the shallow water equations with a bottom step
    • A. Alcrudo and F. Benkhaldoun, Exact solutions to the Riemann problem of the shallow water equations with a bottom step, Computers & Fluids, 30, 643-671, 2001.
    • (2001) Computers & Fluids , vol.30 , pp. 643-671
    • Alcrudo, A.1    Benkhaldoun, F.2
  • 2
    • 1642367583 scopus 로고    scopus 로고
    • Godunov-type approximation for a general resonant balance law with large data
    • D. Amadori, L. Gosse and G. Guerra, Godunov-type approximation for a general resonant balance law with large data, J. Diff. Equ., 198, 233-274, 2004.
    • (2004) J. Diff. Equ , vol.198 , pp. 233-274
    • Amadori, D.1    Gosse, L.2    Guerra, G.3
  • 3
    • 3142733781 scopus 로고    scopus 로고
    • On the solution to the Riemann problem for the compressible duct flow
    • N. Andrianov and G. Warnecke, On the solution to the Riemann problem for the compressible duct flow, SIAM J. Appl. Math., 64(3), 878-901, 2004.
    • (2004) SIAM J. Appl. Math , vol.64 , Issue.3 , pp. 878-901
    • Andrianov, N.1    Warnecke, G.2
  • 4
    • 4644342716 scopus 로고    scopus 로고
    • A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows
    • E. Audusse, F. Bouchut, M.O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comp., 25(6), 2050-2065, 2004.
    • (2004) SIAM J. Sci. Comp , vol.25 , Issue.6 , pp. 2050-2065
    • Audusse, E.1    Bouchut, F.2    Bristeau, M.O.3    Klein, R.4    Perthame, B.5
  • 7
    • 0001522672 scopus 로고
    • Definition and weak stability of nonconservative products
    • G. Dal Maso, P.G. LeFloch and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl., 74, 483-548, 1995.
    • (1995) J. Math. Pures Appl , vol.74 , pp. 483-548
    • Dal Maso, G.1    LeFloch, P.G.2    Murat, F.3
  • 8
    • 5744239576 scopus 로고    scopus 로고
    • The Riemann problem for a class of resonant nonlinear systems of balance laws
    • P. Goatin and P.G. LeFloch, The Riemann problem for a class of resonant nonlinear systems of balance laws, Ann. Inst. H. Poincaré Anal. Nonlinéaire, 21, 881-902, 2004.
    • (2004) Ann. Inst. H. Poincaré Anal. Nonlinéaire , vol.21 , pp. 881-902
    • Goatin, P.1    LeFloch, P.G.2
  • 9
    • 0036013523 scopus 로고    scopus 로고
    • Localization effects and measure source terms in numerical schemes for balance laws
    • L. Gosse, Localization effects and measure source terms in numerical schemes for balance laws, Math. Comp., 71, 553-582, 2002.
    • (2002) Math. Comp , vol.71 , pp. 553-582
    • Gosse, L.1
  • 10
    • 4544386272 scopus 로고    scopus 로고
    • Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation
    • L. Gosse and G. Toscani, Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation, Numer. Math., 98(2), 223-250, 2004.
    • (2004) Numer. Math , vol.98 , Issue.2 , pp. 223-250
    • Gosse, L.1    Toscani, G.2
  • 11
  • 12
    • 0034345304 scopus 로고    scopus 로고
    • Nonclassical shock waves and kinetic relations: Strictly hyperbolic systems
    • B.T. Hayes and P.G. LeFloch, Nonclassical shock waves and kinetic relations: Strictly hyperbolic systems, SIAM J. Math. Anal., 31, 941-991, 2000.
    • (2000) SIAM J. Math. Anal , vol.31 , pp. 941-991
    • Hayes, B.T.1    LeFloch, P.G.2
  • 13
    • 84968497746 scopus 로고
    • Why nonconservative schemes converge to wrong solutions: Error analysis
    • T.Y. Hou and P.G. LeFloch, Why nonconservative schemes converge to wrong solutions: error analysis, Math. Comp., 62, 497-530, 1994.
    • (1994) Math. Comp , vol.62 , pp. 497-530
    • Hou, T.Y.1    LeFloch, P.G.2
  • 14
    • 0026931381 scopus 로고
    • Nonlinear resonance in systems of conservation laws
    • E. Isaacson and B. Temple, Nonlinear resonance in systems of conservation laws, SIAM J. Appl. Math., 52, 1260-1278, 1992.
    • (1992) SIAM J. Appl. Math , vol.52 , pp. 1260-1278
    • Isaacson, E.1    Temple, B.2
  • 15
    • 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, 625-640, 1995.
    • (1995) SIAM J. Appl. Math , vol.55 , pp. 625-640
    • Isaacson, E.1    Temple, B.2
  • 16
    • 33646472331 scopus 로고    scopus 로고
    • Numerical solutions to compressible flows in a nozzle with variable cross-section
    • D. Kröner and M.D. Thanh, Numerical solutions to compressible flows in a nozzle with variable cross-section, SIAM J. Numer. Anal., 43(2), 796-824, 2005.
    • (2005) SIAM J. Numer. Anal , vol.43 , Issue.2 , pp. 796-824
    • Kröner, D.1    Thanh, M.D.2
  • 17
    • 85036919587 scopus 로고    scopus 로고
    • P.D. Lax, Shock waves and entropy, in: E.H. Zarantonello, Contributions to Nonlinear Functional Analysis, 603-634, 1971.
    • P.D. Lax, Shock waves and entropy, in: E.H. Zarantonello, Contributions to Nonlinear Functional Analysis, 603-634, 1971.
  • 20
    • 21344434180 scopus 로고    scopus 로고
    • Graph solutions of nonlinear hyperbolic systems
    • P.G. LeFloch, Graph solutions of nonlinear hyperbolic systems, J. Hyper. Diff. Equa., 1, 643-689, 2004.
    • (2004) J. Hyper. Diff. Equa , vol.1 , pp. 643-689
    • LeFloch, P.G.1
  • 21
    • 5744243501 scopus 로고    scopus 로고
    • The Riemann problem for fluid flows in a nozzle with discontinuous cross-section
    • P.G. LeFloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section, Commun. Math. Sci., 1(4), 763-797, 2003.
    • (2003) Commun. Math. Sci , vol.1 , Issue.4 , pp. 763-797
    • LeFloch, P.G.1    Thanh, M.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.