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Global simulations using MHD codes: A few points to consider before you try one

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Abstract

A survey of all global time-dependent MHD simulations is presented. The survey includes a discussion of the physical situations simulated by the respective authors as well as the numerical algorithms employed. Finally a discussion of the advantages enjoyed by certain numerical schemes and the problems that a researcher will very likely encounter if he should undertake construction of such codes is presented.

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References

  • Boris, J.P., and D.L. Book, ‘Flux-corrected transport, 1, SHASTA, a transport algorithm that works,’ J. Comp. Phys., 11, 38, 1973.

    Google Scholar 

  • Boris, J.P., ‘Physically motivated solution of the Alfven problem,’ Naval Res. Lab. Memo. Rept. No. 2167, 1970.

  • Brackbill, J.U., and D.C. Barnes, ‘The effect of non-zero ▽·B on the numerical solutions of the magnetohydrodynamic equations,’ J. Comp. Phys., 35. 426, 1980.

    ADS  MathSciNet  Google Scholar 

  • Brecht, S.H., J.G. Lyon, J.A. Fedder, and P.J. Palmadesso, ‘Comments on plasma dynamics in the earth's magnetotail,’ Comments Plasma Phys. and Controlled Fusion, 6, 59, 1980.

    Google Scholar 

  • Brecht, S.H., J.G. Lyon, J.A. Fedder, and K. Hain, ‘A simulation study of east-west IMF effects on the magnetosphere,’ Geophys. Res. Lett., 8, 397, 1981.

    ADS  Google Scholar 

  • Brecht, S.H., J.G. Lyon, J.A. Fedder, and K. Hain, ‘A time dependent three dimensional simulation of the earth's magnetosphere: Reconnection events,’ J. Geophys. Res., 87, 6098, 1982.

    ADS  Google Scholar 

  • Brecht, S.H. and D.F. Smith, ‘Three-dimensional simulations of the Venusian magnetosphere,’ EOS Trans., AGU, 65, 1041, 1984.

    Google Scholar 

  • Cowley, S.W.H., ‘Magnetospheric asymmetries associated with the y-component of the IMF,’ Planet. Space Sci., 29, 79, 1981.

    ADS  Google Scholar 

  • Dryer, M., S.T. Wu, G. Gislason, S.M. Han, Z.K. Smith., J.F. Wang, D.F. Smart and M.A. Shea, ‘Magnetohydrodynamic modelling of interplanetary disturbances between the sun and earth,’ Astrophys. and Space Sci., 105, 187, 1984.

    ADS  Google Scholar 

  • Dungey, J.W., ‘Interplanetary magnetic field and the auroral zone,’ Phys. Rev. Lett., 6, 47, 1961.

    Article  ADS  Google Scholar 

  • Fedder, J.A., S.H. Brecht, and J.G. Lyon, ‘MHD simulation of a comet magnetosphere,’ (submitted to Icarus, 1984) NRL Memo. Rpt. No. 5306, 1984a.

  • Fedder, J.A. and J.G. Lyon, ‘Region 1 Birkland currents from a global simulation of the magnetosphere,’ (in press JGR) NRL Memo. Rpt. No. 5397, 1984b.

  • Godunov, S.K., ‘Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics,’ Matematichekii Sbornik, 47, 271, 1959.

    MATH  MathSciNet  Google Scholar 

  • Hain, K., ‘The partial donor cell method,’ NRL Memo. Rpt. No. 3713, Naval Res. Lab., Wash., D.C., 1978.

  • Hardy, D.A., H.K. Hills and J.W. Freeman, ‘Occurrence of the lobe plasma at lunar distances,’ J. Geophys. Res., 84, 72, 1979.

    ADS  Google Scholar 

  • Hones, E.W., Jr., ‘Plasma flow in the plasma sheet and its relation to substorms,’ Radio Sci., 8, 979, 1973.

    Google Scholar 

  • Hones, E.W., Jr., D.N. Baker, S.J. Bame, W.C. Feldman, J.T. Gosling, D.J. McComas, R.D. Zwickl, J.A. Slavin, E.J. Smith, and B.T. Tsurutani, ‘Structure of the magnetotail at 220 RE and its response to geomagnetic activity,’ Geophys. Res. Lett., 11, 5, 1984.

    ADS  Google Scholar 

  • Lax, P.D., “Weak solution of nonlinear hyperbolic equations and their numerical computation,” Commun. Pure Appl. Math., 17, 159, 1954.

    MathSciNet  Google Scholar 

  • LeBoeuf, J.N., T. Tajima, C.F. Kennel and J.M. Dawson, ‘Global simulations of the time-dependent magnetosphere,’ Geophys. Res. Lett., 5, 609, 1978.

    ADS  Google Scholar 

  • LeBoeuf, J.N., T. Tajima, C.F. Kennel and J.M. Dawson, ‘Global simulations of the three-dimensional magnetosphere,’ Geophys. Res. Lett., 8, 257, 1981.

    ADS  Google Scholar 

  • Lui, A.T.Y., ‘Observations on plasma sheet dynamics during magnetospheric substorms,’ in Dynamics of the Magnetosphere, pp. 563–597, D. Reidel, Hingham, Mass., 1979.

    Google Scholar 

  • Lyon, J., S.H. Brecht, J.A. Fedder, and P.J. Palmadesso, ‘The effect on the earth's magnetotail from shocks in the solar wind,’ Geophys. Res. Lett., 7, 712, 1980.

    Google Scholar 

  • Lyon, J., S.H. Brecht, J.D. Huba, J.A. Fedder, and P.J. Palmadesso, ‘Computer simulation of a geomagnetic substrom,’ Phys. Rev. Lett., 46, 1038, 1981.

    Article  ADS  Google Scholar 

  • McPherron, R.L., C.T. Russell and M.P. Aubry, ‘Phenomenological model for substorms,’ J. Geophys. Res., 78, 3131, 1973.

    Google Scholar 

  • Ogino, T. and R.J. Walker, ‘An MHD simulation of the bifurcation of the tail lobes during intervals with northward interplanetary magnetic field,’ UCLA Rpt. PPG-782, 1984a.

  • Ogino, T. ‘A three-dimensional MHD simulation of the interaction of the solar wind with the earth's magnetosphere: The generation of field aligned currents,’ UCLA Rpt. PPG-796, 1984b.

  • Ogino, T., R.J. Walker, M. Ashour-Abdalla and J.M. Dawson, ‘An MHD simulation of By -dependent magnetospheric convection and field aligned currents during northward IMF,’ UCLA Rpt. PPG-805, 1984c.

  • Roach, P.J., Computational Fluid Dynamics, 5th Ed. Hermosa Publishers, P.O. Box 8172, Albuquerque, NM 87108, 1982.

    Google Scholar 

  • Schmidt, H.U. and R. Wegman, ‘MHD-calculations for cometary plasmas,’ Comp. Phys. Comm., 19, 309, 1980.

    ADS  Google Scholar 

  • Wolf, R.A., M. Harel, R.W. Spiro, G.-H. Voigt, P.H. Reiff, and C.-K. Chen, ‘Computer simulation of inner magnetospheric dynamics for the magnetic storm of July 29, 1977,’ J. Geophys. Res., 87, 5949, 1982.

    ADS  Google Scholar 

  • Woodward, P. and P. Colella, ‘The numerical simulation of two-dimensional fluid flow with strong shocks,’ J. Comp. Phys., 54, 115, 1984.

    ADS  MathSciNet  Google Scholar 

  • Wu, C.C., R.J. Walker, and J.M. Dawson, ‘A three-dimensional MHD model of the earth's magnetosphere,’ Geophys. Res. Lett., 8, 525, 1981.

    ADS  Google Scholar 

  • Wu, S.T., M. Dryer, and S.M. Han, ‘Non-planar MHD model for solar flare-generated disturbances in the heliospheric equatorial plane,’ Solar Physics, 84, 395, 1983.

    Article  ADS  Google Scholar 

  • Zalezak, S.T., ‘Fully multidimensional flux-corrected transport algorithms for fluids,’ J. Comp. Phys., 31, 335, 1979.

    ADS  Google Scholar 

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Brecht, S.H. Global simulations using MHD codes: A few points to consider before you try one. Space Sci Rev 42, 169–185 (1985). https://doi.org/10.1007/BF00218231

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