A new approach for modelling chromospheric evaporation in response to enhanced coronal heating

II. Non-uniform heating

¹ School of Mathematics and Statistics, University of St. Andrews, St. Andrews, Fife, KY16 9SS, UK
e-mail: cdj3@st-andrews.ac.uk
² Space and Atmospheric Physics, The Blackett Laboratory, Imperial College, London, SW7 2BW, UK

Received: 23 January 2017
Accepted: 25 April 2017

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 atmosphere; (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.