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Volumn 74, Issue 1, 1996, Pages 1-33

An entropy satisfying MUSCL scheme for systems of conservation laws

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EID: 0030501943     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050205     Document Type: Article
Times cited : (26)

References (41)
  • 1
    • 48349083249 scopus 로고
    • A second-order Godunov-type scheme for compressible gaz dynamics
    • Ben-Artzi, M., Falcovitz, J.C. (1984): A second-order Godunov-type scheme for compressible gaz dynamics. J. Comp. Phys. 55, 1-32
    • (1984) J. Comp. Phys. , vol.55 , pp. 1-32
    • Ben-Artzi, M.1    Falcovitz, J.C.2
  • 3
    • 0038908816 scopus 로고
    • An example of MUSCL method satisfying all the entropy inequalities
    • Bouchut, F., Bourdarias, C., Perthame, B. (1993): An example of MUSCL method satisfying all the entropy inequalities. C.R. Acad. Sc. Paris. Série I, 317, 619-624
    • (1993) C.R. Acad. Sc. Paris. Série I , vol.317 , pp. 619-624
    • Bouchut, F.1    Bourdarias, C.2    Perthame, B.3
  • 4
    • 0040686631 scopus 로고
    • An asymptotic expansion for the solution of the generalized Riemann problem. Part II: Application to the gas dynamics equations
    • Bourgeade, A., LeFloch, P.G., Raviart, P.-A. (1989): An asymptotic expansion for the solution of the generalized Riemann problem. Part II: application to the gas dynamics equations. Ann. Inst. H. Poincaré, Nonlinear Analysis 6, 437-480
    • (1989) Ann. Inst. H. Poincaré, Nonlinear Analysis , vol.6 , pp. 437-480
    • Bourgeade, A.1    LeFloch, P.G.2    Raviart, P.-A.3
  • 5
    • 0003094692 scopus 로고
    • The one-sided Lipschitz condition for convex scalar conservation laws
    • Brenier, Y., Osher, S. (1988): The one-sided Lipschitz condition for convex scalar conservation laws. SIAM J. Numer. Anal. 25, 8-23
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 8-23
    • Brenier, Y.1    Osher, S.2
  • 7
    • 84990717899 scopus 로고
    • Entropy flux-splittings for hyperbolic conservation laws. Part I: General framework
    • Chen, G.-Q., LeFloch, P.G. (1995): Entropy flux-splittings for hyperbolic conservation laws. Part I: general framework. Comm. Pure Appl. Math. 48, 691-729
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 691-729
    • Chen, G.-Q.1    LeFloch, P.G.2
  • 8
    • 84968467467 scopus 로고
    • Convergence of second-order schemes for isentropic gas dynamics
    • Chen, G.-Q., Liu, J.-G. (1993): Convergence of second-order schemes for isentropic gas dynamics. Math. of Comp. 1993 61, 607-627
    • (1993) Math. of Comp. 1993 , vol.61 , pp. 607-627
    • Chen, G.-Q.1    Liu, J.-G.2
  • 9
    • 84968494859 scopus 로고
    • Error estimates for finite volume methods for multidimensional conservation laws
    • Cockburn, B., Coquel, F., LeFloch, P.G. (1994): Error estimates for finite volume methods for multidimensional conservation laws. Math. of Comp. 63, 77-103
    • (1994) Math. of Comp. , vol.63 , pp. 77-103
    • Cockburn, B.1    Coquel, F.2    LeFloch, P.G.3
  • 10
    • 0000805244 scopus 로고
    • Convergence of finite volume methods for multidimensional conservation laws
    • Cockburn, B., Coquel, F., LeFloch, P.G. (1995): Convergence of finite volume methods for multidimensional conservation laws. SIAM J. Numer. Anal. 32, 687-705
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 687-705
    • Cockburn, B.1    Coquel, F.2    LeFloch, P.G.3
  • 11
    • 34547419627 scopus 로고
    • The piecewise parabolic method (PPM) for gas-dynamical simulations
    • Colella, P., Woodward, P.R. (1984): The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comp. Phys. 54, 174-201
    • (1984) J. Comp. Phys. , vol.54 , pp. 174-201
    • Colella, P.1    Woodward, P.R.2
  • 12
    • 0027608674 scopus 로고
    • Convergence of finite difference schemes for conservation laws in several space variables: A general theory
    • Coquel, F., LeFloch, P.G. (1993): Convergence of finite difference schemes for conservation laws in several space variables: a general theory. SIAM J. Numer. Anal. 30, 675-700
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 675-700
    • Coquel, F.1    LeFloch, P.G.2
  • 13
    • 84966234654 scopus 로고
    • Convergence of finite difference schemes for scalar conservation laws in several space dimensions: The corrected antidiffusive flux approach
    • Coquel, F., LeFloch, P.G. (1991): Convergence of finite difference schemes for scalar conservation laws in several space dimensions: the corrected antidiffusive flux approach. Math. of Comp. 57, 169-210
    • (1991) Math. of Comp. , vol.57 , pp. 169-210
    • Coquel, F.1    LeFloch, P.G.2
  • 16
    • 0002578353 scopus 로고
    • Convergence of the viscosity method for isentropic gas dynamics
    • DiPerna, R.J. (1983): Convergence of the viscosity method for isentropic gas dynamics. Comm. Math. Phys. 91, 1-30
    • (1983) Comm. Math. Phys. , vol.91 , pp. 1-30
    • DiPerna, R.J.1
  • 17
    • 0020499710 scopus 로고
    • Convergence of approximate solutions to conservation laws
    • DiPerna, R.J. (1983): Convergence of approximate solutions to conservation laws. Arch. Rat. Mech. Anal. 82, 27-70
    • (1983) Arch. Rat. Mech. Anal. , vol.82 , pp. 27-70
    • DiPerna, R.J.1
  • 18
    • 84981759861 scopus 로고
    • Solutions in the large for nonlinear hyperbolic systems of equations
    • Glimm, J. (1965): Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18, 697-715
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 697-715
    • Glimm, J.1
  • 19
    • 0000296272 scopus 로고
    • A geometric approach to high resolution TVD schemes
    • Goodman, J., LeVeque, R. (1988): A geometric approach to high resolution TVD schemes. SIAM J. Numer. Anal. 25, 268-284
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 268-284
    • Goodman, J.1    LeVeque, R.2
  • 20
    • 0038908820 scopus 로고
    • The generalized Riemann problem with analytic data
    • Harabetian, E. (1988): The generalized Riemann problem with analytic data. Trans. Amer. Math. Soc.
    • (1988) Trans. Amer. Math. Soc.
    • Harabetian, E.1
  • 21
    • 0021381876 scopus 로고
    • On a class of high order resolution total-variation stable finite difference schemes
    • Harten, A. (1974): On a class of high order resolution total-variation stable finite difference schemes. SIAM J. Numer. Anal. 21, 1-23
    • (1974) SIAM J. Numer. Anal. , vol.21 , pp. 1-23
    • Harten, A.1
  • 22
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially non-oscillatory schemes
    • Harten, A., Engquist, B., Osher, S.J., Chakravarthy, S. (1987): Uniformly high order accurate essentially non-oscillatory schemes. J. Comp. Phys. 71, 231-303
    • (1987) J. Comp. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.J.3    Chakravarthy, S.4
  • 23
    • 84966232205 scopus 로고
    • On the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws
    • Johnson, C., Szepessy A., Hansbo, P. (1990): On the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws. Math. of comp. 54, 107-129
    • (1990) Math. of Comp. , vol.54 , pp. 107-129
    • Johnson, C.1    Szepessy, A.2    Hansbo, P.3
  • 24
    • 84968497598 scopus 로고
    • Maximum principle on the entropy and second-order kinetic schemes
    • Khobalatte, B., Perthame, B. (1994): Maximum principle on the entropy and second-order kinetic schemes. Math. of Comp. 62, 119-135
    • (1994) Math. of Comp. , vol.62 , pp. 119-135
    • Khobalatte, B.1    Perthame, B.2
  • 25
    • 0003261490 scopus 로고
    • Hyperbolic systems of conservation laws and the mathematical theory of shock waves
    • SIAM, Philadelphia
    • Lax, P.D. (1973): Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. Conf. Board Math. Sci. 11, SIAM, Philadelphia
    • (1973) Conf. Board Math. Sci. , pp. 11
    • Lax, P.D.1
  • 26
    • 0038908819 scopus 로고
    • Towards the ultimate conservative difference schemes. V: A second order sequel to Godunov's method
    • Van Leer, B. (1981): Towards the ultimate conservative difference schemes. V: A second order sequel to Godunov's method. J. Comp. Phys. 43, 357-372
    • (1981) J. Comp. Phys. , vol.43 , pp. 357-372
    • Van Leer, B.1
  • 27
    • 0040093141 scopus 로고
    • Discrete entropy and monotonicity criterion for hyperbolic conservation laws
    • LeFloch, P.G., Liu, J.-G. (1994): Discrete entropy and monotonicity criterion for hyperbolic conservation laws. C.R. Acad. Sci., Paris 319, 881-886
    • (1994) C.R. Acad. Sci., Paris , vol.319 , pp. 881-886
    • LeFloch, P.G.1    Liu, J.-G.2
  • 28
    • 0038908817 scopus 로고
    • An asymptotic expansion for the solution of the generalized Riemann problem. Part 1: General theory Ann. Inst. H. Poincaré
    • LeFloch, P.G., Raviart, P.-A. (1988): An asymptotic expansion for the solution of the generalized Riemann problem. Part 1: general theory Ann. Inst. H. Poincaré, Nonlin. Anal. 5, 179-207
    • (1988) Nonlin. Anal. , vol.5 , pp. 179-207
    • LeFloch, P.G.1    Raviart, P.-A.2
  • 29
    • 34249763254 scopus 로고
    • Kinetic formulations for the p-system and Euler system
    • Lions, P.-L., Perthame, B., Tadmor, E. (1994): Kinetic formulations for the p-system and Euler system. Comm. Math. Phys. 163, 415-431
    • (1994) Comm. Math. Phys. , vol.163 , pp. 415-431
    • Lions, P.-L.1    Perthame, B.2    Tadmor, E.3
  • 30
    • 0040686629 scopus 로고
    • Convergence of MUSCL-type methods for scalar conservation laws
    • Lions, P.-L., Sougadinis, P. (1990): Convergence of MUSCL-type methods for scalar conservation laws. C.R. Acad. Sc. Paris, Série I, 311, 259-264
    • (1990) C.R. Acad. Sc. Paris, Série I , vol.311 , pp. 259-264
    • Lions, P.-L.1    Sougadinis, P.2
  • 32
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • Nessyahu, H., Tadmor, E. (1990): Non-oscillatory central differencing for hyperbolic conservation laws. J. Comp. Phys. 87, 408-462
    • (1990) J. Comp. Phys. , vol.87 , pp. 408-462
    • Nessyahu, H.1    Tadmor, E.2
  • 33
    • 0022144821 scopus 로고
    • Convergence of generalized MUSCL schemes
    • Osher, S.J. (1985): Convergence of generalized MUSCL schemes. SIAM J. Numer. Anal. 22, 947-961
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 947-961
    • Osher, S.J.1
  • 34
    • 0022144821 scopus 로고
    • High resolution schemes and entropy condition
    • Osher, S.J., Chakravarthy, S. (1985): High resolution schemes and entropy condition. SIAM J. Numer. Anal. 22, 947-961
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 947-961
    • Osher, S.J.1    Chakravarthy, S.2
  • 35
    • 84966232121 scopus 로고
    • On the convergence of difference approximations to scalar conservation laws
    • Osher, S.J., Tadmor, E. (1988): On the convergence of difference approximations to scalar conservation laws. Math. of Comp. 50, 19-51
    • (1988) Math. of Comp. , vol.50 , pp. 19-51
    • Osher, S.J.1    Tadmor, E.2
  • 36
    • 0040686628 scopus 로고
    • Domaines invariants pour les systèmes hyperboliques de lois de conservation
    • Serre, D. (1987): Domaines invariants pour les systèmes hyperboliques de lois de conservation. J. Diff. Eq. 69, 46-62
    • (1987) J. Diff. Eq. , vol.69 , pp. 46-62
    • Serre, D.1
  • 38
    • 0000546289 scopus 로고
    • The numerical viscosity of entropy stable schemes for systems of conservation laws
    • Tadmor, E. (1987): The numerical viscosity of entropy stable schemes for systems of conservation laws. Math. of Comp. 49, 91-103
    • (1987) Math. of Comp. , vol.49 , pp. 91-103
    • Tadmor, E.1
  • 39
    • 0039501482 scopus 로고
    • ∞-stability imply convergence
    • ∞-stability imply convergence. ICASE Report 88-41
    • (1988) ICASE Report , pp. 88-141
    • Tadmor, E.1
  • 40
    • 0040093142 scopus 로고
    • High-order schemes and the entropy condition for ronlinear hyperbolic systems of conservation laws
    • Vila, J.P. (1988): High-order schemes and the entropy condition for ronlinear hyperbolic systems of conservation laws. Math. of Comp. 50, 53-73
    • (1988) Math. of Comp. , vol.50 , pp. 53-73
    • Vila, J.P.1


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