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Volumn 46, Issue 5, 2004, Pages 457-484

Non-oscillatory relaxation methods for the shallow-water equations in one and two space dimensions

Author keywords

Higher order non oscillatory schemes; Relaxation methods; Runge Kutta methods; Shallow water equations

Indexed keywords

FLOW OF FLUIDS; MATHEMATICAL MODELS; PROBLEM SOLVING; SURFACE TOPOGRAPHY;

EID: 5044227412     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.766     Document Type: Article
Times cited : (50)

References (33)
  • 1
    • 0003933895 scopus 로고
    • Interscience Publishers, Inc.: New York
    • Stoker JJ. Water Waves. Interscience Publishers, Inc.: New York, -1986.
    • (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, Navarro PG. A high resolution Godunov-type scheme in finite volumes for the 2D shallow water equations. International Journal for Numerical Methods in Fluids 1993; 16:489-505.
    • (1993) International Journal for Numerical Methods in Fluids , vol.16 , pp. 489-505
    • Alcrudo, F.1    Navarro, P.G.2
  • 6
    • 0037404907 scopus 로고    scopus 로고
    • Some approximate Godunov schemes to compute shallow water equations with topography
    • Gallouët T, Herard JM, Seguin N. Some approximate Godunov schemes to compute shallow water equations with topography. Computers and Fluids 2003; 32:479-513.
    • (2003) Computers and Fluids , vol.32 , pp. 479-513
    • Gallouët, T.1    Herard, J.M.2    Seguin, N.3
  • 8
    • 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. Journal of Computational Physics 1998; 146:346-365.
    • (1998) Journal of Computational Physics , vol.146 , pp. 346-365
    • LeVeque Randall, J.1
  • 10
    • 84990701264 scopus 로고
    • The relaxation schemes for systems of conservation laws in arbitrary space dimensions
    • Jin S, Xin Z. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Communications on Pure and Applied Mathematics 1995; 48:235-276.
    • (1995) Communications on Pure and Applied Mathematics , vol.48 , pp. 235-276
    • Jin, S.1    Xin, Z.2
  • 11
    • 85065353078 scopus 로고    scopus 로고
    • Convergence of relaxation scheme for conservation laws
    • Aregba-Driollet D, Natalini R. Convergence of relaxation scheme for conservation laws. Applicable Analysis 1996; 61:163-193.
    • (1996) Applicable Analysis , vol.61 , pp. 163-193
    • Aregba-Driollet, D.1    Natalini, R.2
  • 12
    • 0006388461 scopus 로고    scopus 로고
    • Convergence of relaxation scheme for hyperbolic conservation laws with stiff source terms
    • Chalabi A. Convergence of relaxation scheme for hyperbolic conservation laws with stiff source terms. Mathematics of Computation 1999; 68:955-970.
    • (1999) Mathematics of Computation , vol.68 , pp. 955-970
    • Chalabi, A.1
  • 14
    • 0000136945 scopus 로고    scopus 로고
    • Convergence rates for relaxation schemes approximating conservation laws
    • Liu HL, Warnecke G. Convergence rates for relaxation schemes approximating conservation laws. SIAM Journal on Numerical Analysis 2000; 37:1316-1337.
    • (2000) SIAM Journal on Numerical Analysis , vol.37 , pp. 1316-1337
    • Liu, H.L.1    Warnecke, G.2
  • 15
    • 0002936886 scopus 로고    scopus 로고
    • Relaxation schemes for a Lattice-Boltzmann type discrete velocity model and numerical Navier-Stokes limit
    • Klar A. Relaxation schemes for a Lattice-Boltzmann type discrete velocity model and numerical Navier-Stokes limit. Journal of Computational Physics 1999; 148:1-17.
    • (1999) Journal of Computational Physics , vol.148 , pp. 1-17
    • Klar, A.1
  • 16
    • 0030490070 scopus 로고    scopus 로고
    • Convergence to equilibrium for relaxation approximations of conservation laws
    • Natalini R. Convergence to equilibrium for relaxation approximations of conservation laws. Communications on Pure and Applied Mathematics 1996; 49:795-823.
    • (1996) Communications on Pure and Applied Mathematics , vol.49 , pp. 795-823
    • Natalini, R.1
  • 17
    • 0034688726 scopus 로고    scopus 로고
    • Relaxation limit for piecewise smooth solutions to conservation laws
    • Xu WQ. Relaxation limit for piecewise smooth solutions to conservation laws. Journal of Differential Equations 2000; 162:140-173.
    • (2000) Journal of Differential Equations , vol.162 , pp. 140-173
    • Xu, W.Q.1
  • 18
    • 0035581884 scopus 로고    scopus 로고
    • Convergence of a relaxation scheme for hyperbolic systems of conservation laws
    • Lattanzio C, Serre D. Convergence of a relaxation scheme for hyperbolic systems of conservation laws. Numerische Mathematik 2001; 88:121-134.
    • (2001) Numerische Mathematik , vol.88 , pp. 121-134
    • Lattanzio, C.1    Serre, D.2
  • 19
    • 23044532621 scopus 로고    scopus 로고
    • A class of the relaxation schemes for two-dimensional Euler systems of gas dynamics
    • Banda MK, Seaïd M. A class of the relaxation schemes for two-dimensional Euler systems of gas dynamics. Lecture Notes in Computer Science 2002; 2329:930-939.
    • (2002) Lecture Notes in Computer Science , vol.2329 , pp. 930-939
    • Banda, M.K.1    Seaïd, M.2
  • 20
    • 0034634860 scopus 로고    scopus 로고
    • Zero reaction limit for hyperbolic conservation laws with source terms
    • Fan H, Jin S, Teng Z. Zero reaction limit for hyperbolic conservation laws with source terms. Journal of Differential Equations 2000; 168:270-294.
    • (2000) Journal of Differential Equations , vol.168 , pp. 270-294
    • Fan, H.1    Jin, S.2    Teng, Z.3
  • 21
    • 0034436875 scopus 로고    scopus 로고
    • Uniformly accurate diffusive relaxation schemes for multiscale transport equations
    • Jin S, Pareschi L, Toscani G. Uniformly accurate diffusive relaxation schemes for multiscale transport equations. SIAM Journal on Numerical Analysis 2000; 38:913-936.
    • (2000) SIAM Journal on Numerical Analysis , vol.38 , pp. 913-936
    • Jin, S.1    Pareschi, L.2    Toscani, G.3
  • 23
    • 0034879339 scopus 로고    scopus 로고
    • A third-order semi-discrete central scheme for conservation laws and convection-diffusion equations
    • Kurganov A, Levy D. A third-order semi-discrete central scheme for conservation laws and convection-diffusion equations. SIAM Journal on Scientific Computing 2000; 22:1461-1488.
    • (2000) SIAM Journal on Scientific Computing , vol.22 , pp. 1461-1488
    • Kurganov, A.1    Levy, D.2
  • 24
    • 0035075926 scopus 로고    scopus 로고
    • Compact central WENO schemes for multidimensional conservation laws
    • Levy D, Puppo G, Russo G. Compact central WENO schemes for multidimensional conservation laws. SIAM Journal on Scientific Computing 2000; 22:656-672.
    • (2000) SIAM Journal on Scientific Computing , vol.22 , pp. 656-672
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 25
    • 0031269714 scopus 로고    scopus 로고
    • Implicit explicit Runge-Kutta methods for time-dependent partial differential equations
    • Ascher U, Ruuth S, Spiteri R. Implicit explicit Runge-Kutta methods for time-dependent partial differential equations. Applied Numerical Mathematics 1997; 25:151-167.
    • (1997) Applied Numerical Mathematics , vol.25 , pp. 151-167
    • Ascher, U.1    Ruuth, S.2    Spiteri, R.3
  • 26
    • 0012148580 scopus 로고    scopus 로고
    • Implicit-Explicit Runge Kutta schemes for stiff systems of differential equations
    • Pareschi L, Russo G. Implicit-Explicit Runge Kutta schemes for stiff systems of differential equations. Recent Trends in Numerical Analysis 2000; 3:269-289.
    • (2000) Recent Trends in Numerical Analysis , vol.3 , pp. 269-289
    • Pareschi, L.1    Russo, G.2
  • 27
    • 28844475047 scopus 로고    scopus 로고
    • Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
    • in press
    • Pareschi L, Russo G. Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. Journal of Scientific Computing, in press.
    • Journal of Scientific Computing
    • Pareschi, L.1    Russo, G.2
  • 29
    • 0344950457 scopus 로고    scopus 로고
    • Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique
    • Brufau P, García-Navarro P. Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique. Journal of Computational Physics 2003; 186:503-526.
    • (2003) Journal of Computational Physics , vol.186 , pp. 503-526
    • Brufau, P.1    García-Navarro, P.2
  • 31
    • 0028534347 scopus 로고
    • Upwind methods for hyperbolic conservation laws with source terms
    • Bermudez A, Vázquez-Cendón ME. Upwind methods for hyperbolic conservation laws with source terms. Computers & Fluids 1994; 23:1049-1071.
    • (1994) Computers and Fluids , vol.23 , pp. 1049-1071
    • Bermudez, A.1    Vázquez-Cendón, M.E.2
  • 32
    • 0001528721 scopus 로고    scopus 로고
    • Solution of two-dimensional Riemann problems of gas dynamics by positive schemes
    • Lax P, Liu X. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAM Journal on Scientific Computing 1998; 19:319-340.
    • (1998) SIAM Journal on Scientific Computing , vol.19 , pp. 319-340
    • Lax, P.1    Liu, X.2
  • 33
    • 0030171562 scopus 로고    scopus 로고
    • Essentially compact schemes for unsteady viscous incompressible flows
    • Weinan E, Liu JG. Essentially compact schemes for unsteady viscous incompressible flows. Journal of Computational Physics 1996; 126:122-138.
    • (1996) Journal of Computational Physics , vol.126 , pp. 122-138
    • Weinan, E.1    Liu, J.G.2


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