Modelling the solar transition region using an adaptive conduction method

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
³ Rosseland Centre for Solar Physics, University of Oslo, PO Box 1029, Blindern 0315 Oslo, Norway
⁴ Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA

Received: 23 October 2019
Accepted: 25 February 2020

Abstract

Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and transition region, when the corona undergoes impulsive heating. The TRAC method eliminates the need for highly resolved numerical grids in the transition region and the commensurate very short time steps that are required for numerical stability. When employed with coarse spatial resolutions, typically achieved in multi-dimensional magnetohydrodynamic codes, the errors at peak density are less than 5% and the computation time is three orders of magnitude faster than fully resolved field-aligned models. This paper presents further examples that demonstrate the versatility and robustness of the method over a range of heating events, including impulsive and quasi-steady footpoint heating. A detailed analytical assessment of the TRAC method is also presented, showing that the approach works through all phases of an impulsive heating event because (i) the total radiative losses and (ii) the total heating when integrated over the transition region are both preserved at all temperatures under the broadening modifications of the method. The results from the numerical simulations complement this conclusion.