Abstract
We proposed that the use of an approximate "jump condition" at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of non-uniform heating, in particular, nanoflare trains (uniform in space but non-uniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (i) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmsophere, (ii) mass motions at the base of the transition region and (iii) for some cases with footpoint heating, an over-estimation of the radiative losses in the transition region.
Highlights
By using one-dimensional (1D) hydrodynamic models to study the physics of magnetically confined coronal loops, we have learned a great deal about the temporal response of coronal loop plasma to heating
In Paper I we demonstrate that this new approach obtains coronal densities comparable to fully resolved 1D models (e.g. BC13) but with computation times that are between one and two orders of magnitude faster, since the computational timestep is not limited by thermal conduction in the transition region (TR)
We introduced the jump condition approach for 1D hydrodynamic modelling in Paper I
Summary
By using one-dimensional (1D) hydrodynamic (field-aligned) models to study the physics of magnetically confined coronal loops (see e.g. Reale 2014, for a review), we have learned a great deal about the temporal response of coronal loop plasma to heating. LT can be less than 1km for a loop in thermal equilibrium and even shorter in hot flaring loops, because of the steep temperature dependence of thermal conduction and the location of the peak of the radiative losses between 105 and 106 K Resolving these small length scales is essential in order to obtain the correct coronal density in response to time dependent heating (Bradshaw & Cargill 2013, hereafter BC13). In Paper I we demonstrate that this new approach obtains coronal densities comparable to fully resolved 1D models (e.g. BC13) but with computation times that are between one and two orders of magnitude faster, since the computational timestep is not limited by thermal conduction in the TR. Different (spatially non-uniform) heating functions and initial plasma conditions in order for future users to have confidence in the model The latter is addressed through consideration of a nanoflare train.
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