Efficient numerical treatment of ambipolar and Hall drift as hyperbolic system

Abstract

Partially ionized plasmas, such as the solar chromosphere, require a generalized Ohm's law including the effects of ambipolar and Hall drift. While both describe transport processes that arise from the multifluid equations and are therefore of hyperbolic nature, they are often incorporated in models as a diffusive, i.e. parabolic process. While the formulation as such is easy to include in standard MHD models, the resulting diffusive time-step constraints do require often a computationally more expensive implicit treatment or super-time-stepping approaches. In this paper we discuss an implementation that retains the hyperbolic nature and allows for an explicit integration with small computational overhead. In the case of ambipolar drift, this formulation arises naturally by simply retaining a time derivative of the drift velocity that is typically omitted. This alone leads to time-step constraints that are comparable to the native MHD time-step constraint for a solar setup including the region from photosphere to lower solar corona. We discuss an accelerated treatment that can further reduce time-step constraints if necessary. In the case of Hall drift we propose a hyperbolic formulation that is numerically similar to that for the ambipolar drift and we show that the combination of both can be applied to simulations of the solar chromosphere at minimal computational expense.

arXiv comment21 pages, 13 figures, accepted for publication in ApJ

References in corpus (15)

• The chemical composition of the Sun
• Numerical simulations of quiet Sun magnetism: On the contribution from a small-scale dynamo
• Extension of the MURaM radiative MHD code for coronal simulations
• Hall magnetohydrodynamics of partially ionized plasmas
• 2D Radiative MHD Simulations of the Importance of Partial Ionization in the Chromosphere
• Energy flux of Alfven waves in weakly ionized plasma
• A three-dimensional numerical method for modelling weakly ionized plasmas
• Magnetohydrodynamics of the Weakly Ionized Solar Photosphere
• MHD simulations of the eruption of coronal flux ropes under coronal streamers
• Effect of coronal temperature on the scale of solar chromospheric jets
• MHDSTS: a new explicit numerical scheme for simulations of partially ionised solar plasma
• Nonequilibrium ionization and ambipolar diffusion in solar magnetic flux emergence processes
• Fast-to-Alfvén Mode Conversion Mediated by Hall Current. I. Cold Plasma Model
• Ambipolar diffusion in the Bifrost code
• Fast Recursive Reconnection and the Hall effect: Hall-MHD Simulations

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• Structure and dynamics of the internetwork solar chromosphere: results of a small-scale dynamo simulation
• The Relation between Solar Spicules and Magnetohydrodynamic Shocks
• Modeling of Chromospheric Features and Dynamics in Solar Plage