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A numerical magnetohydrodynamic scheme using the hydrostatic approximation


  • Jonathan Braithwaite,

    Corresponding author
    • Argelander Institut für Astronomie, Universität Bonn, Bonn, Germany
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  • Yuri Cavecchi

    1. Astronomical Institute ‘Anton Pannekoek’, University of Amsterdam, 1090 GE Amsterdam, the Netherlands
    2. Sterrewacht Leiden, University of Leiden, CA Leiden, the Netherlands
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In gravitationally stratified fluids, length scales are normally much greater in the horizontal direction than in the vertical one. When modelling these fluids it can be advantageous to use the hydrostatic approximation, which filters out vertically propagating sound waves and thus allows a greater time-step. We briefly review this approximation, which is commonplace in atmospheric physics, and compare it to other approximations used in astrophysics such as Boussinesq and anelastic, finding that it should be the best approximation to use in context such as radiative stellar zones, compact objects, stellar or planetary atmospheres and other contexts. We describe a finite-difference numerical scheme which uses this approximation, which includes magnetic fields.