  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.
