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Volumn 39, Issue 3, 1999, Pages 451-472

Unconditionally stable splitting methods for the shallow water equations

Author keywords

Front tracking; Grid refinement; Operator splitting; Shallow water equations

Indexed keywords


EID: 0000628580     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022366502335     Document Type: Article
Times cited : (26)

References (37)
  • 1
    • 0027561554 scopus 로고
    • A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations
    • F. Alcrudo and P. Garcia-Navarro, A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations, Internat. J. Numer. Methods Fluids, 16 (1993), pp. 489-505.
    • (1993) Internat. J. Numer. Methods Fluids , vol.16 , pp. 489-505
    • Alcrudo, F.1    Garcia-Navarro, P.2
  • 2
    • 0028976397 scopus 로고
    • Approximation of shallow water equations by Roe's Riemann solver
    • D. Ambrosi, Approximation of shallow water equations by Roe's Riemann solver, Internat. J. Numer. Methods Fluids, 20 (1995), pp. 157-168.
    • (1995) Internat. J. Numer. Methods Fluids , vol.20 , pp. 157-168
    • Ambrosi, D.1
  • 3
    • 0032030398 scopus 로고    scopus 로고
    • Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes
    • A. Bermùdez, A. Dervieux, J. A. Désidéri, and M. E. Vázquez, Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes, Comput. Methods Appl. Mech. Engrg., 155 (1998), pp. 49-72.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.155 , pp. 49-72
    • Bermùdez, A.1    Dervieux, A.2    Désidéri, J.A.3    Vázquez, M.E.4
  • 4
    • 0006338644 scopus 로고    scopus 로고
    • Well-posedness of the Cauchy problem for n × n systems of conservation laws
    • to appear
    • A. Bressan, G. Crasta, and B. Piccoli, Well-posedness of the Cauchy problem for n × n systems of conservation laws, Mem. Amer. Math. Soc., to appear
    • Mem. Amer. Math. Soc.
    • Bressan, A.1    Crasta, G.2    Piccoli, B.3
  • 5
    • 0031295331 scopus 로고    scopus 로고
    • Uniqueness of weak solutions to systems of conservation laws
    • A. Bressan and P. LeFloch, Uniqueness of weak solutions to systems of conservation laws, Arch. Rational Mech. Anal., 140:4 (1997), pp. 301-317.
    • (1997) Arch. Rational Mech. Anal. , vol.140 , Issue.4 , pp. 301-317
    • Bressan, A.1    LeFloch, P.2
  • 6
    • 0025473498 scopus 로고
    • Explicit methods for 2-D transient free-surface flows
    • R. J. Fennema and M. H. Chaudhry, Explicit methods for 2-D transient free-surface flows, J. Hydraul. Eng., 116 (1990), pp. 1013-1034.
    • (1990) J. Hydraul. Eng. , vol.116 , pp. 1013-1034
    • Fennema, R.J.1    Chaudhry, M.H.2
  • 8
    • 0041935750 scopus 로고    scopus 로고
    • A front tracking method for conservation laws in two dimensions
    • H. Holden, K.-A. Lie, and N. H. Risebro, A front tracking method for conservation laws in two dimensions, J. Comput. Phys., 150 (1999), pp. 76-96.
    • (1999) J. Comput. Phys. , vol.150 , pp. 76-96
    • Holden, H.1    Lie, K.-A.2    Risebro, N.H.3
  • 9
    • 84968505714 scopus 로고
    • A method of fractional steps for scalar conservation laws without the CFL condition
    • H. Holden and N. H. Risebro, A method of fractional steps for scalar conservation laws without the CFL condition, Math. Comp., 60(201) (1993), pp. 221-232.
    • (1993) Math. Comp. , vol.60 , Issue.201 , pp. 221-232
    • Holden, H.1    Risebro, N.H.2
  • 10
    • 0004304885 scopus 로고    scopus 로고
    • Lecture Notes, Department of Mathematical Sciences, Norwegian University of Science and Technology
    • H. Holden and N. H. Risebro, Front Tracking for Conservation Laws, Lecture Notes, Department of Mathematical Sciences, Norwegian University of Science and Technology.
    • Front Tracking for Conservation Laws
    • Holden, H.1    Risebro, N.H.2
  • 11
    • 0032206542 scopus 로고    scopus 로고
    • Nonoscillatory central schemes for multidimensional hyperbolic conservation laws
    • G.-S. Jiang and E. Tadmor, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput., 19:6 (1998), pp. 1892-1917.
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.6 , pp. 1892-1917
    • Jiang, G.-S.1    Tadmor, E.2
  • 12
    • 0030173370 scopus 로고    scopus 로고
    • On an implementation of a front tracking method for hyperbolic conservation laws
    • J. O. Langseth, On an implementation of a front tracking method for hyperbolic conservation laws, Advances in Engineering Software, 26:1 (1996), pp. 45-63.
    • (1996) Advances in Engineering Software , vol.26 , Issue.1 , pp. 45-63
    • Langseth, J.O.1
  • 14
    • 0022388409 scopus 로고
    • Large time step shock-capturing techniques for scalar conservation laws
    • R. J. LeVeque, Large time step shock-capturing techniques for scalar conservation laws, SIAM J. Numer. Anal., 22 (1985), pp. 1051-1073.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 1051-1073
    • Leveque, R.J.1
  • 17
    • 0000308880 scopus 로고    scopus 로고
    • Wave propagation algorithms for multidimensional hyperbolic systems
    • R. J. LeVeque, Wave propagation algorithms for multidimensional hyperbolic systems, J. Comput. Phys. 131 (1997), pp. 327-353.
    • (1997) J. Comput. Phys. , vol.131 , pp. 327-353
    • LeVeque, R.J.1
  • 18
    • 0000087732 scopus 로고
    • One-dimensional front tracking based on high resolution wave propagation methods
    • R. J. LeVeque and K. M. Shyue, One-dimensional front tracking based on high resolution wave propagation methods, SIAM J. Sci. Comput., 16:2 (1995), pp. 348-377.
    • (1995) SIAM J. Sci. Comput. , vol.16 , Issue.2 , pp. 348-377
    • LeVeque, R.J.1    Shyue, K.M.2
  • 21
    • 0005464911 scopus 로고
    • Nonhydrostatic two-layer models of incompressible flow
    • R. Liska, L. Margolin, and B. Wendroff, Nonhydrostatic two-layer models of incompressible flow, Comput. Math. Appl., 29 (1995), pp. 25-37.
    • (1995) Comput. Math. Appl. , vol.29 , pp. 25-37
    • Liska, R.1    Margolin, L.2    Wendroff, B.3
  • 22
    • 0000088242 scopus 로고    scopus 로고
    • Composite schemes for conservation laws
    • R. Liska and B. Wendroff, Composite schemes for conservation laws, SIAM J. Numer. Anal., 35 (1998), pp. 2250-2271.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2250-2271
    • Liska, R.1    Wendroff, B.2
  • 23
    • 0012220845 scopus 로고    scopus 로고
    • 2D shallow water equations by composite schemes
    • to appear
    • R. Liska and B. Wendroff, 2D shallow water equations by composite schemes, J. Num. Meth. Fluids, to appear.
    • J. Num. Meth. Fluids
    • Liska, R.1    Wendroff, B.2
  • 24
    • 0040653659 scopus 로고    scopus 로고
    • Analysis and computation with stratified fluid models
    • R. Liska and B. Wendroff, Analysis and computation with stratified fluid models, J. Comput. Phys., 137:1 (1997), pp. 212-244.
    • (1997) J. Comput. Phys. , vol.137 , Issue.1 , pp. 212-244
    • Liska, R.1    Wendroff, B.2
  • 25
    • 0000710622 scopus 로고
    • On the vacuum state for isentropic gas dynamics
    • T.-P. Liu and J. Smoller, On the vacuum state for isentropic gas dynamics, Adv. Pure Appl. Math., 1 (1980), pp. 345-359.
    • (1980) Adv. Pure Appl. Math. , vol.1 , pp. 345-359
    • Liu, T.-P.1    Smoller, J.2
  • 27
    • 0026186036 scopus 로고
    • Mathematical modeling of a snow-powder avalanche in the framework of the equations of two-layer shallow water
    • A. N. Nazarov, Mathematical modeling of a snow-powder avalanche in the framework of the equations of two-layer shallow water, Fluid Dynamics, 26 (1991), pp. 70-75.
    • (1991) Fluid Dynamics , vol.26 , pp. 70-75
    • Nazarov, A.N.1
  • 28
    • 84966257267 scopus 로고
    • A front-tracking alternative to the random choice method
    • N. H. Risebro, A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc, 117:4 (1993), pp. 1125-1129.
    • (1993) Proc. Amer. Math. Soc , vol.117 , Issue.4 , pp. 1125-1129
    • Risebro, N.H.1
  • 29
    • 0001502445 scopus 로고
    • Front tracking applied to a nonstrictly hyperbolic system of conservation laws
    • N. H. Risebro and A. Tveito, Front tracking applied to a nonstrictly hyperbolic system of conservation laws, SIAM J. Sci. Stat. Comput., 12:6 (1991), pp. 1401-1419.
    • (1991) SIAM J. Sci. Stat. Comput. , vol.12 , Issue.6 , pp. 1401-1419
    • Risebro, N.H.1    Tveito, A.2
  • 30
    • 0001027457 scopus 로고
    • A front tracking method for conservation laws in one dimension
    • N. H. Risebro and A. Tveito, A front tracking method for conservation laws in one dimension, J. Comput. Phys., 101:1 (1992), pp. 130-139.
    • (1992) J. Comput. Phys. , vol.101 , Issue.1 , pp. 130-139
    • Risebro, N.H.1    Tveito, A.2
  • 31
    • 38249040792 scopus 로고
    • AZTEC: A front tracking code based on Godunov's method
    • B. K. Swartz and B. Wendroff, AZTEC: a front tracking code based on Godunov's method, Appl. Numer. Math., 2:3-5 (1986), pp. 385-397.
    • (1986) Appl. Numer. Math. , vol.2 , Issue.3-5 , pp. 385-397
    • Swartz, B.K.1    Wendroff, B.2
  • 32
    • 0019382973 scopus 로고
    • Some exact solutions to the nonlinear shallow-water wave equations
    • W. C. Thacker, Some exact solutions to the nonlinear shallow-water wave equations, J. Fluid Mech., 107 (1981), pp. 499-508.
    • (1981) J. Fluid Mech. , vol.107 , pp. 499-508
    • Thacker, W.C.1
  • 33
    • 0002203252 scopus 로고
    • Riemann problems and the WAF method for solving the two-dimensional shallow water equations
    • E. F. Toro, Riemann problems and the WAF method for solving the two-dimensional shallow water equations, Philos. Trans. Roy. Soc. London Ser. A., 338 (1992), pp. 43-68.
    • (1992) Philos. Trans. Roy. Soc. London Ser. A. , vol.338 , pp. 43-68
    • Toro, E.F.1
  • 35
    • 0031512558 scopus 로고    scopus 로고
    • A unified Riemann-problem-based extension of the Warming-Beam and Lax-Wendroff schemes
    • E. F. Toro and S. J. Billett, A unified Riemann-problem-based extension of the Warming-Beam and Lax-Wendroff schemes, IMA J. Numer. Anal., 17 (1997), pp. 61-102.
    • (1997) IMA J. Numer. Anal. , vol.17 , pp. 61-102
    • Toro, E.F.1    Billett, S.J.2
  • 36
    • 0018314831 scopus 로고
    • Two-layer shallow-water flow in two dimensions, a numerical study
    • C. B. Vreugdenhil, Two-layer shallow-water flow in two dimensions, a numerical study, J. Comput. Phys., 33 (1979), pp. 169-184.
    • (1979) J. Comput. Phys. , vol.33 , pp. 169-184
    • Vreugdenhil, C.B.1
  • 37
    • 0004419270 scopus 로고
    • An analysis of front tracking for chromatography
    • B. Wendroff, An analysis of front tracking for chromatography, Acta Appl. Math., 30 (1993), pp. 265-285.
    • (1993) Acta Appl. Math. , vol.30 , pp. 265-285
    • Wendroff, B.1


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