  We present a new computational approach that addresses the difficulty of
obtaining the correct interaction between the solar corona and the transition
region in response to rapid heating events. In the coupled corona, transition
region and chromosphere system, an enhanced downward conductive flux results in
an upflow (chromospheric evaporation). However, obtaining the correct upflow
generally requires high spatial resolution in order to resolve the transition
region. With an unresolved transition region, artificially low coronal
densities are obtained because the downward heat flux jumps across the
unresolved region to the chromosphere, underestimating the upflows. Here, we
treat the lower transition region as a discontinuity that responds to changing
coronal conditions through the imposition of a jump condition that is derived
from an integrated form of energy conservation. To illustrate and benchmark
this approach against a fully resolved one-dimensional model, we present
field-aligned simulations of coronal loops in response to a range of impulsive
(spatially uniform) heating events. We show that our approach leads to a
significant improvement in the coronal density evolution than just when using
coarse spatial resolutions insufficient to resolve the lower transition region.
Our approach compensates for the jumping of the heat flux by imposing a
velocity correction that ensures that the energy from the heat flux goes into
driving the transition region dynamics, rather than being lost through
radiation. Hence, it is possible to obtain improved coronal densities. The
advantages of using this approach in both one-dimensional hydrodynamic and
three-dimensional magnetohydrodynamic simulations are discussed.
