  Large-scale coronal plasma evolutions can be adequately described by
magnetohydrodynamics (MHD) equations. However, full multi-dimensional MHD
simulations require substantial computational resources. Given the low plasma
$\beta$ in the solar corona, in many coronal studies, it suffices to
approximate the magnetic field to remain topologically fixed and effectively
conduct one-dimensional (1D) hydrodynamic (HD) simulations instead. This
approach is often employed in studies of coronal loops and their liability to
form condensations related to thermal instability. While 1D HD simulations
along given and fixed field line shapes are convenient and fast, they are
difficult to directly compare with multi-dimensional phenomena. Therefore, it
is more convenient to solve volume-filling, multi-dimensional versions of the
MHD equations where we freeze the magnetic field, transforming it into
frozen-field HD (ffHD) equations for simulation. We have incorporated this ffHD
module into our open-source MPI-AMRVAC code and tested it using a
two-dimensional (2D) evaporation--condensation model to study prominence
formation due to radiative losses. The 2D ffHD results are compared with those
from actual 2D MHD and pseudo-2D HD simulations, analyzing the differences and
their causes. Pseudo-2D studies account for the known {flux tube} expansion
effects. Overall, the performance of 2D ffHD is close to that of 2D MHD and
pseudo-2D HD. The 2D tests conducted in this paper will be extended in
follow-up studies to 3D simulations based on analytical or observational
approaches.
