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.
Similar content being viewed by others
References
Boris, J.P., and D.L. Book, ‘Flux-corrected transport, 1, SHASTA, a transport algorithm that works,’ J. Comp. Phys., 11, 38, 1973.
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.
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.
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.
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.
Brecht, S.H. and D.F. Smith, ‘Three-dimensional simulations of the Venusian magnetosphere,’ EOS Trans., AGU, 65, 1041, 1984.
Cowley, S.W.H., ‘Magnetospheric asymmetries associated with the y-component of the IMF,’ Planet. Space Sci., 29, 79, 1981.
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.
Dungey, J.W., ‘Interplanetary magnetic field and the auroral zone,’ Phys. Rev. Lett., 6, 47, 1961.
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.
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.
Hones, E.W., Jr., ‘Plasma flow in the plasma sheet and its relation to substorms,’ Radio Sci., 8, 979, 1973.
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.
Lax, P.D., “Weak solution of nonlinear hyperbolic equations and their numerical computation,” Commun. Pure Appl. Math., 17, 159, 1954.
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.
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.
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.
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.
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.
McPherron, R.L., C.T. Russell and M.P. Aubry, ‘Phenomenological model for substorms,’ J. Geophys. Res., 78, 3131, 1973.
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.
Schmidt, H.U. and R. Wegman, ‘MHD-calculations for cometary plasmas,’ Comp. Phys. Comm., 19, 309, 1980.
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.
Woodward, P. and P. Colella, ‘The numerical simulation of two-dimensional fluid flow with strong shocks,’ J. Comp. Phys., 54, 115, 1984.
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.
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.
Zalezak, S.T., ‘Fully multidimensional flux-corrected transport algorithms for fluids,’ J. Comp. Phys., 31, 335, 1979.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1007/BF00218231