메뉴 건너뛰기




Volumn 147, Issue 2, 1998, Pages 545-567

On Godunov-type schemes for magnetohydrodynamics: 1. A model system

Author keywords

Conservation laws; Godunov type schemes; Magnetohydrodynamics

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS; SHOCK WAVES;

EID: 0000368002     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6101     Document Type: Article
Times cited : (35)

References (45)
  • 2
    • 0040597993 scopus 로고
    • The motion of a conducting piston in a magnetohydrodynamic medium
    • Akhiezer A. I., Polovin R. V. The motion of a conducting piston in a magnetohydrodynamic medium. Soviet Phys.-JETP. 11:1960;383.
    • (1960) Soviet Phys.-JETP , vol.11 , pp. 383
    • Akhiezer, A.I.1    Polovin, R.V.2
  • 3
    • 0031139086 scopus 로고    scopus 로고
    • Developing numerical fluxes with new sonic fix for MHD equations
    • Aslan N., Kammash T. Developing numerical fluxes with new sonic fix for MHD equations. J. Comput. Phys. 133:1997;43.
    • (1997) J. Comput. Phys. , vol.133 , pp. 43
    • Aslan, N.1    Kammash, T.2
  • 5
    • 0030161576 scopus 로고    scopus 로고
    • Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics
    • Barmin A. A., Kulikovskiy A. G., Pogorelov N. V. Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics. J. Comput. Phys. 126:1996;77.
    • (1996) J. Comput. Phys. , vol.126 , pp. 77
    • Barmin, A.A.1    Kulikovskiy, A.G.2    Pogorelov, N.V.3
  • 8
    • 45449121905 scopus 로고
    • An upwind differencing scheme for the equations of ideal magnetohydrodynamics
    • Brio M., Wu C. C. An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 75:1988;400.
    • (1988) J. Comput. Phys. , vol.75 , pp. 400
    • Brio, M.1    Wu, C.C.2
  • 9
    • 0010873221 scopus 로고
    • A Roe solver for the magnetohydrodynamics equations
    • Cargo P., Gallice G. A Roe solver for the magnetohydrodynamics equations. C.R. Acad. Sci. I-Math. 320:1995;1269.
    • (1995) C.R. Acad. Sci. I-Math. , vol.320 , pp. 1269
    • Cargo, P.1    Gallice, G.2
  • 10
    • 0031571997 scopus 로고    scopus 로고
    • Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws
    • Cargo P., Gallice G. Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws. J. Comput. Phys. 136:1997;446.
    • (1997) J. Comput. Phys. , vol.136 , pp. 446
    • Cargo, P.1    Gallice, G.2
  • 12
    • 84980156126 scopus 로고
    • On the structure of magnetohydrodynamic shock waves
    • Conley C. C., Smoller J. A. On the structure of magnetohydrodynamic shock waves. Comm. Pure Appl. Math. 27:1974;367.
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 367
    • Conley, C.C.1    Smoller, J.A.2
  • 13
    • 28144445934 scopus 로고
    • An approximate Riemann solver for ideal magnetohydrodynamics
    • Dai W., Woodward P. R. An approximate Riemann solver for ideal magnetohydrodynamics. J. Comput. Phys. 111:1994;354.
    • (1994) J. Comput. Phys. , vol.111 , pp. 354
    • Dai, W.1    Woodward, P.R.2
  • 14
    • 0003161948 scopus 로고
    • A simple Riemann solver and high-order Godunov scheme for hyperbolic systems of conservation laws
    • Dai W., Woodward P. R. A simple Riemann solver and high-order Godunov scheme for hyperbolic systems of conservation laws. J. Comput. Phys. 121:1995;51.
    • (1995) J. Comput. Phys. , vol.121 , pp. 51
    • Dai, W.1    Woodward, P.R.2
  • 16
    • 0030115579 scopus 로고    scopus 로고
    • Capturing shock reflections: An improved flux function
    • Donat R., Marquina A. Capturing shock reflections: An improved flux function. J. Comput. Phys. 125:1996;42.
    • (1996) J. Comput. Phys. , vol.125 , pp. 42
    • Donat, R.1    Marquina, A.2
  • 17
    • 0342339294 scopus 로고
    • Some remarks on the structure of intermediate magnetohydrodynamic shocks
    • Freistühler H. Some remarks on the structure of intermediate magnetohydrodynamic shocks. J. Geophys. Res. 96:1991;3825.
    • (1991) J. Geophys. Res. , vol.96 , pp. 3825
    • Freistühler, H.1
  • 18
    • 0000986770 scopus 로고
    • A numerical study of a rotationally degenerate hyperbolic system. Part I. The Riemann problem
    • Freistühler H., Pitman E. B. A numerical study of a rotationally degenerate hyperbolic system. Part I. The Riemann problem. J. Comput. Phys. 100:1992;306.
    • (1992) J. Comput. Phys. , vol.100 , pp. 306
    • Freistühler, H.1    Pitman, E.B.2
  • 19
    • 0040004733 scopus 로고
    • A numerical study of a rotationally degenerate hyperbolic system. Part II. The Cauchy problem
    • Freistühler H., Pitman E. B. A numerical study of a rotationally degenerate hyperbolic system. Part II. The Cauchy problem. SIAM J. Numer. Anal. 32:1995;741.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 741
    • Freistühler, H.1    Pitman, E.B.2
  • 20
    • 0343208895 scopus 로고
    • Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves
    • Freistühler H., Szmolyan P. Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves. SIAM J. Math. Anal. 26:1995;112.
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 112
    • Freistühler, H.1    Szmolyan, P.2
  • 21
    • 0038344250 scopus 로고
    • Shock waves and shock-wave structure in magneto-fluid dynamics
    • Germain P. Shock waves and shock-wave structure in magneto-fluid dynamics. Rev. Mod. Phys. 32:1960;951.
    • (1960) Rev. Mod. Phys. , vol.32 , pp. 951
    • Germain, P.1
  • 22
    • 0000935266 scopus 로고
    • Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics
    • Godunov S. K. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47:1959;271.
    • (1959) Mat. Sb. , vol.47 , pp. 271
    • Godunov, S.K.1
  • 23
    • 0005603429 scopus 로고
    • Evolution of large-amplitude Alfvén waves in the solar-wind with beta-similar-to 1
    • Hada T. Evolution of large-amplitude Alfvén waves in the solar-wind with beta-similar-to 1. Geophys. Res. Lett. 20:1993;2415.
    • (1993) Geophys. Res. Lett. , vol.20 , pp. 2415
    • Hada, T.1
  • 24
    • 48749145227 scopus 로고
    • Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
    • Harten A., Hyman J. M. Self-adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comput. Phys. 50:1983;235.
    • (1983) J. Comput. Phys. , vol.50 , pp. 235
    • Harten, A.1    Hyman, J.M.2
  • 26
    • 0001383243 scopus 로고
    • The Riemann problem near a hyperbolic singularity: The classification of solutions of quadratic Riemann problems I
    • Isaacson E., Marchesin D., Plohr B., Temple B. The Riemann problem near a hyperbolic singularity: The classification of solutions of quadratic Riemann problems I. SIAM J. Appl. Math. 48:1988;1009.
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 1009
    • Isaacson, E.1    Marchesin, D.2    Plohr, B.3    Temple, B.4
  • 28
    • 84980077727 scopus 로고
    • Hyperbolic system of conservation laws II
    • Lax P. Hyperbolic system of conservation laws II. Comm. Pure Appl. Math. 10:1957;537.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 537
    • Lax, P.1
  • 29
    • 0009007124 scopus 로고    scopus 로고
    • Magnetohydrodynamic discontinuities in space plasmas: Interrelation between stability and structure
    • Markovskii S. A., Somov B. V. Magnetohydrodynamic discontinuities in space plasmas: Interrelation between stability and structure. Space Sci. Rev. 78:1996;443.
    • (1996) Space Sci. Rev. , vol.78 , pp. 443
    • Markovskii, S.A.1    Somov, B.V.2
  • 30
    • 0031275636 scopus 로고    scopus 로고
    • Analytical results on MHD intermediate shocks
    • Myong R. S. Analytical results on MHD intermediate shocks. Geophys. Res. Lett. 24:1997;2929.
    • (1997) Geophys. Res. Lett. , vol.24 , pp. 2929
    • Myong, R.S.1
  • 31
    • 0031247889 scopus 로고    scopus 로고
    • Shock waves and rarefaction waves in magnetohydrodynamics. Part 1. A model system
    • Myong R. S., Roe P. L. Shock waves and rarefaction waves in magnetohydrodynamics. Part 1. A model system. J. Plasma Phys. 58:1997;485.
    • (1997) J. Plasma Phys. , vol.58 , pp. 485
    • Myong, R.S.1    Roe, P.L.2
  • 32
    • 0031248910 scopus 로고    scopus 로고
    • Shock waves and rarefaction waves in magnetohydrodynamics. Part 2. The MHD system
    • Myong R. S., Roe P. L. Shock waves and rarefaction waves in magnetohydrodynamics. Part 2. The MHD system. J. Plasma Phys. 58:1997;521.
    • (1997) J. Plasma Phys. , vol.58 , pp. 521
    • Myong, R.S.1    Roe, P.L.2
  • 35
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
    • (1981) J. Comput. Phys. , vol.43 , pp. 357
    • Roe, P.L.1
  • 36
    • 0022477699 scopus 로고
    • Characteristic-based schemes for the Euler equations
    • Roe P. L. Characteristic-based schemes for the Euler equations. Ann. Rev. Fluid Mech. 18:1986;337.
    • (1986) Ann. Rev. Fluid Mech. , vol.18 , pp. 337
    • Roe, P.L.1
  • 38
    • 0030087226 scopus 로고    scopus 로고
    • Notes on the eigensystem of magnetohydrodynamics
    • Roe P. L., Balsara D. S. Notes on the eigensystem of magnetohydrodynamics. SIAM J. Appl. Math. 56:1996;57.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 57
    • Roe, P.L.1    Balsara, D.S.2
  • 39
    • 0000814788 scopus 로고
    • The solution of nonstrictly hyperbolic conservation laws may be hard to compute
    • Tveito A., Winther R. The solution of nonstrictly hyperbolic conservation laws may be hard to compute. SIAM J. Sci. Comput. 16:1995;320.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 320
    • Tveito, A.1    Winther, R.2
  • 40
    • 34249988639 scopus 로고
    • Towards the ultimate conservative difference scheme, II. Monotonicity and conservation combined in a second-order scheme
    • van Leer B. Towards the ultimate conservative difference scheme, II. Monotonicity and conservation combined in a second-order scheme. J. Comput. Phys. 14:1974;361.
    • (1974) J. Comput. Phys. , vol.14 , pp. 361
    • Van Leer, B.1
  • 41
    • 15444376171 scopus 로고
    • A numerical implementation of MHD in divergence form
    • van Putten M. H. P. M. A numerical implementation of MHD in divergence form. J. Comput. Phys. 105:1993;339.
    • (1993) J. Comput. Phys. , vol.105 , pp. 339
    • Van Putten, M.H.P.M.1
  • 43
    • 84989558401 scopus 로고
    • On MHD intermediate shocks
    • Wu C. C. On MHD intermediate shocks. Geophys. Res. Lett. 14:1987;668.
    • (1987) Geophys. Res. Lett. , vol.14 , pp. 668
    • Wu, C.C.1
  • 44
    • 0040597992 scopus 로고
    • Intermediate shocks
    • Wu C. C. Intermediate shocks. Phys. Scripta. T60:1995;97.
    • (1995) Phys. Scripta , vol.60 , pp. 97
    • Wu, C.C.1
  • 45
    • 0000008663 scopus 로고
    • A higher-order Godunov method for the equations of ideal magnetohydrodynamics
    • Zachary A. L., Colella P. A higher-order Godunov method for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 99:1992;341.
    • (1992) J. Comput. Phys. , vol.99 , pp. 341
    • Zachary, A.L.1    Colella, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.