A fast multi-dimensional magnetohydrodynamic formulation of the transition region adaptive conduction (TRAC) method. (arXiv:2106.03989v2 [astro-ph.SR] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Johnston_C/0/1/0/all/0/1">C. D. Johnston</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hood_A/0/1/0/all/0/1">A. W. Hood</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Moortel_I/0/1/0/all/0/1">I. De Moortel</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pagano_P/0/1/0/all/0/1">P. Pagano</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Howson_T/0/1/0/all/0/1">T. A. Howson</a>
We have demonstrated that the Transition Region Adaptive Conduction (TRAC)
method permits fast and accurate numerical solutions of the field-aligned
hydrodynamic equations, successfully removing the influence of numerical
resolution on the coronal density response to impulsive heating. This is
achieved by adjusting the parallel thermal conductivity, radiative loss, and
heating rates to broaden the transition region (TR), below a global cutoff
temperature, so that the steep gradients are spatially resolved even when using
coarse numerical grids. Implementing the original 1D formulation of TRAC in
multi-dimensional magnetohydrodynamic (MHD) models would require tracing a
large number of magnetic field lines at every time step in order to prescribe a
global cutoff temperature to each field line. In this paper, we present a
highly efficient formulation of the TRAC method for use in multi-dimensional
MHD simulations, which does not rely on field line tracing. In the TR, adaptive
local cutoff temperatures are used instead of global cutoff temperatures to
broaden any unresolved parts of the atmosphere. These local cutoff temperatures
are calculated using only local grid cell quantities, enabling the MHD
extension of TRAC to efficiently account for the magnetic field evolution,
without tracing field lines. Consistent with analytical predictions, we show
that this approach successfully preserves the properties of the original TRAC
method. In particular, the total radiative losses and heating remain conserved
under the MHD formulation. Results from 2D MHD simulations of impulsive heating
in unsheared and sheared arcades of coronal loops are also presented. These
simulations benchmark the MHD TRAC method against a series of 1D models and
demonstrate the versatility and robustness of the method in multi-dimensional
magnetic fields. We show, for the first time, that pressure differences, …
We have demonstrated that the Transition Region Adaptive Conduction (TRAC)
method permits fast and accurate numerical solutions of the field-aligned
hydrodynamic equations, successfully removing the influence of numerical
resolution on the coronal density response to impulsive heating. This is
achieved by adjusting the parallel thermal conductivity, radiative loss, and
heating rates to broaden the transition region (TR), below a global cutoff
temperature, so that the steep gradients are spatially resolved even when using
coarse numerical grids. Implementing the original 1D formulation of TRAC in
multi-dimensional magnetohydrodynamic (MHD) models would require tracing a
large number of magnetic field lines at every time step in order to prescribe a
global cutoff temperature to each field line. In this paper, we present a
highly efficient formulation of the TRAC method for use in multi-dimensional
MHD simulations, which does not rely on field line tracing. In the TR, adaptive
local cutoff temperatures are used instead of global cutoff temperatures to
broaden any unresolved parts of the atmosphere. These local cutoff temperatures
are calculated using only local grid cell quantities, enabling the MHD
extension of TRAC to efficiently account for the magnetic field evolution,
without tracing field lines. Consistent with analytical predictions, we show
that this approach successfully preserves the properties of the original TRAC
method. In particular, the total radiative losses and heating remain conserved
under the MHD formulation. Results from 2D MHD simulations of impulsive heating
in unsheared and sheared arcades of coronal loops are also presented. These
simulations benchmark the MHD TRAC method against a series of 1D models and
demonstrate the versatility and robustness of the method in multi-dimensional
magnetic fields. We show, for the first time, that pressure differences, …
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