  The brightness of the emission from coronal loops in the solar atmosphere is
strongly dependent on the temperature and density of the confined plasma. After
a release of energy, these loops undergo a heating and upflow phase, followed
by a cooling and downflow cycle. Throughout, there are significant variations
in the properties of the coronal plasma. In particular, the increased coronal
temperature leads to an excess downward heat flux that the transition region is
unable to radiate. This generates an enthalpy flux from the transition region
to the corona, increasing the coronal density. The enthalpy exchange is highly
sensitive to the transition region resolution in numerical simulations. With a
numerically under-resolved transition region, major errors occur in simulating
the coronal density evolution and, thus, the predicted loop emission. This
Letter presents a new method that addresses the difficulty of obtaining the
correct interaction between the corona and corona/chromosphere interface. In
the transition region, an adaptive thermal conduction approach is used that
broadens any unresolved parts of the atmosphere. We show that this approach,
referred to as TRAC, successfully removes the influence of numerical resolution
on the coronal density response to heating while maintaining high levels of
agreement with fully resolved models. When employed with coarse spatial
resolutions, typically achieved in multi-dimensional MHD codes, the peak
density errors are less than 3% and the computation time is three orders of
magnitude faster than fully resolved field-aligned models. The advantages of
using TRAC in field-aligned hydrodynamic and multi-dimensional
magnetohydrodynamic simulations are discussed.
