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Volumn 142, Issue 2, 1998, Pages 331-369

A Simple Finite Difference Scheme for Multidimensional Magnetohydrodynamical Equations

Author keywords

Finite difference; Godunov scheme; Hyperbolic system; MHD simulation

Indexed keywords

MAGNETOHYDRODYNAMICS;

EID: 0001580138     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.5944     Document Type: Article
Times cited : (162)

References (40)
  • 1
    • 0000935266 scopus 로고
    • Difference methods for the numerical calculation of the equations of fluid dynamics
    • Godunov S. K. Difference methods for the numerical calculation of the equations of fluid dynamics. Math. Sb. 47:1959;271.
    • (1959) Math. Sb. , vol.47 , pp. 271
    • Godunov, S.K.1
  • 4
    • 0001518684 scopus 로고
    • On construction and comparison of differential schemes
    • Strang G. On construction and comparison of differential schemes. SIAM J. Numer. Anal. 5:1968;506.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 506
    • Strang, G.1
  • 6
    • 2442433925 scopus 로고
    • Toward the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
    • Van Leer B. Toward the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 32:1979;101.
    • (1979) J. Comput. Phys. , vol.32 , pp. 101
    • Van Leer, B.1
  • 7
    • 0018286867 scopus 로고
    • Small-scale structure of two-dimensional magnetohydrodynamic turbulence
    • Orszag S. A., Tang C.-M. Small-scale structure of two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 90:1979;129.
    • (1979) J. Fluid Mech. , vol.90 , pp. 129
    • Orszag, S.A.1    Tang, C.-M.2
  • 9
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameters vectors, and difference schemes
    • Roe P. L. Approximate Riemann solvers, parameters vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
    • (1981) J. Comput. Phys. , vol.43 , pp. 357
    • Roe, P.L.1
  • 11
    • 0000030941 scopus 로고
    • High resolution difference schemes for compressible gas dynamics
    • Woodward P. R., Colella P. High resolution difference schemes for compressible gas dynamics. Lecture Notes in Phys. 141:1981;434.
    • (1981) Lecture Notes in Phys. , vol.141 , pp. 434
    • Woodward, P.R.1    Colella, P.2
  • 12
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:1983;357.
    • (1983) J. Comput. Phys. , vol.49 , pp. 357
    • Harten, A.1
  • 13
    • 48749139407 scopus 로고
    • The numerical simulation of two-dimensional fluid flow with strong shocks
    • Woodward P. R., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54:1984;115.
    • (1984) J. Comput. Phys. , vol.54 , pp. 115
    • Woodward, P.R.1    Colella, P.2
  • 14
    • 34547419627 scopus 로고
    • The piecewise parabolic method (PPM) for gas-dynamical simulations
    • Colella P., Woodward P. R. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54:1984;174.
    • (1984) J. Comput. Phys. , vol.54 , pp. 174
    • Colella, P.1    Woodward, P.R.2
  • 15
    • 0023329384 scopus 로고
    • Uniformly high order accurate non-oscillatory schemes, I
    • Harten A., Osher S. Uniformly high order accurate non-oscillatory schemes, I. SIAM J. Numer. Anal. 24:1987;279.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 279
    • Harten, A.1    Osher, S.2
  • 16
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially non-oscillatory schemes, III
    • Harten A., Enquist B., Osher S., Chakravarthy S. R. Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys. 71:1987;231.
    • (1987) J. Comput. Phys. , vol.71 , pp. 231
    • Harten, A.1    Enquist, B.2    Osher, S.3    Chakravarthy, S.R.4
  • 17
    • 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
  • 18
    • 0002258785 scopus 로고
    • High resolution finite volume methods on arbitrary grids via wave propagation
    • LeVeque R. High resolution finite volume methods on arbitrary grids via wave propagation. J. Comput. Phys. 78:1988;36.
    • (1988) J. Comput. Phys. , vol.78 , pp. 36
    • Leveque, R.1
  • 19
    • 0000194504 scopus 로고
    • Simulation of Magnetohydrodynamic flows: A constrained transport method
    • Evans C., Hawley J. F. Simulation of Magnetohydrodynamic flows: A constrained transport method. Astrophys. J. 332:1988;659.
    • (1988) Astrophys. J. , vol.332 , pp. 659
    • Evans, C.1    Hawley, J.F.2
  • 20
    • 0000236567 scopus 로고
    • Evolution of the Orszag-Tang vortex system in a compressible medium. I. Initial average subsonic flow
    • Dahlburg R. B., Picone J. M. Evolution of the Orszag-Tang vortex system in a compressible medium. I. Initial average subsonic flow. Phys. Fluid B. 1:1989;2153.
    • (1989) Phys. Fluid B , vol.1 , pp. 2153
    • Dahlburg, R.B.1    Picone, J.M.2
  • 21
    • 0000494892 scopus 로고
    • Higher order Godunov methods for general systems of hyperbolic conservation laws
    • Bell J. B., Colella P., Trangenstein J. A. Higher order Godunov methods for general systems of hyperbolic conservation laws. J. Comput. Phys. 82:1989;362.
    • (1989) J. Comput. Phys. , vol.82 , pp. 362
    • Bell, J.B.1    Colella, P.2    Trangenstein, J.A.3
  • 22
    • 26844455510 scopus 로고
    • Multidimensional upwind methods for hyperbolic conservation laws
    • Colella P. Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys. 87:1990;171.
    • (1990) J. Comput. Phys. , vol.87 , pp. 171
    • Colella, P.1
  • 23
    • 0002634491 scopus 로고
    • Evolution of the Orszag-Tang vortex system in a compressible medium. II. Supersonic flow
    • Picone J. M., Dahlburg R. B. Evolution of the Orszag-Tang vortex system in a compressible medium. II. Supersonic flow. Phys. Fluid B. 3:1991;29.
    • (1991) Phys. Fluid B , vol.3 , pp. 29
    • Picone, J.M.1    Dahlburg, R.B.2
  • 25
    • 0000008663 scopus 로고
    • A high-order Godunov method for the equations of ideal magnetohydrodynamics
    • Zachary A. L., Colella P. A high-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
  • 26
    • 4243869796 scopus 로고
    • ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. II. The magnetohydrodynamics algorithms and tests
    • Stone J. M., Norman M. L. ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. II. The magnetohydrodynamics algorithms and tests. Astrophys. J. Supl. 80:1992;791.
    • (1992) Astrophys. J. Supl. , vol.80 , pp. 791
    • Stone, J.M.1    Norman, M.L.2
  • 27
    • 0003332686 scopus 로고
    • Numerical solution of the Riemann problem for two-dimensional gas dynamics
    • Schulz-Rinne C. W., Collins J. P., Glaz H. M. Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAM J. Sci. Comput. 14:1993;1394.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1394
    • Schulz-Rinne, C.W.1    Collins, J.P.2    Glaz, H.M.3
  • 28
    • 0002531306 scopus 로고
    • An unsplit 3D upwind method for hyperbolic conservation laws
    • Saltzman J. An unsplit 3D upwind method for hyperbolic conservation laws. J. Comput. Phys. 115:1994;153.
    • (1994) J. Comput. Phys. , vol.115 , pp. 153
    • Saltzman, J.1
  • 29
    • 0000128492 scopus 로고
    • A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
    • Zachary A. L., Malagoli A., Colella P. A higher-order Godunov method for multidimensional ideal magnetohydrodynamics. SIAM J. Sci. Comput. 15:1994;263.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 263
    • Zachary, A.L.1    Malagoli, A.2    Colella, P.3
  • 30
    • 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
  • 31
    • 0042487895 scopus 로고
    • Extension of the piecewise parabolic method (PPM) to multidimensional ideal magnetohydrodynamics
    • Dai W., Woodward P. R. Extension of the piecewise parabolic method (PPM) to multidimensional ideal magnetohydrodynamics. J. Comput. Phys. 115:1994;485.
    • (1994) J. Comput. Phys. , vol.115 , pp. 485
    • Dai, W.1    Woodward, P.R.2
  • 34
    • 11944265404 scopus 로고
    • Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for one-dimensional flow
    • Ryu D., Jones T. W. Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for one-dimensional flow. Astrophys. J. 442:1995;228.
    • (1995) Astrophys. J. , vol.442 , pp. 228
    • Ryu, D.1    Jones, T.W.2
  • 35
    • 0000489153 scopus 로고
    • Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for multidimensional flow
    • Ryu D., Jones T. W., Frank A. Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for multidimensional flow. Astrophys. J. 452:1995;785.
    • (1995) Astrophys. J. , vol.452 , pp. 785
    • Ryu, D.1    Jones, T.W.2    Frank, A.3
  • 36
    • 0029277387 scopus 로고
    • Numerical simulation of the MHD equations by a kinetic-type method
    • Croisille J.-P., Khanfir R., Chanteur G. Numerical simulation of the MHD equations by a kinetic-type method. J. Sci. Comput. 10:1995;81.
    • (1995) J. Sci. Comput. , vol.10 , pp. 81
    • Croisille, J.-P.1    Khanfir, R.2    Chanteur, G.3
  • 37
    • 0003161948 scopus 로고
    • A simple Riemann solver and high-order Godunov schemes for hyperbolic systems of conservation laws
    • Dai W., Woodward P. R. A simple Riemann solver and high-order Godunov schemes for hyperbolic systems of conservation laws. J. of Comput. Phys. 121:1995;51.
    • (1995) J. of Comput. Phys. , vol.121 , pp. 51
    • Dai, W.1    Woodward, P.R.2
  • 38
    • 0030075590 scopus 로고    scopus 로고
    • Two-dimensional front tracking based on high resolution wave propagation methods
    • LeVeque R. J., Shyue K.-M. Two-dimensional front tracking based on high resolution wave propagation methods. J. Comput. Phys. 123:1996;354.
    • (1996) J. Comput. Phys. , vol.123 , pp. 354
    • Leveque, R.J.1    Shyue, K.-M.2
  • 39
    • 0040069139 scopus 로고    scopus 로고
    • Total variation diminishing scheme for magnetohydrodynamics
    • D. Balsara, Total variation diminishing scheme for magnetohydrodynamics, J. Comput. Phys.
    • J. Comput. Phys.
    • Balsara, D.1
  • 40
    • 0031185310 scopus 로고    scopus 로고
    • A second-order unsplit Godunov scheme for two- And three-dimensional Euler equations
    • Dai W., Woodward P. R. A second-order unsplit Godunov scheme for two- and three-dimensional Euler equations. J. Comput. Phys. 134:1997;261.
    • (1997) J. Comput. Phys. , vol.134 , pp. 261
    • Dai, W.1    Woodward, P.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.