  Radiation transport problems are posed in a high-dimensional phase space,
limiting the use of finely resolved numerical simulations. An emerging tool to
efficiently reduce computational costs and memory footprint in such settings is
dynamical low-rank approximation (DLRA). Despite its efficiency, numerical
methods for DLRA need to be carefully constructed to guarantee stability while
preserving crucial properties of the original problem. Important physical
effects that one likes to preserve with DLRA include capturing the diffusion
limit in the high-scattering regimes as well as dissipating energy. In this
work we propose and analyze a dynamical low-rank method based on the
"unconventional" basis-update & Galerkin step integrator. We show that this
method is asymptotic-preserving, i.e., it captures the diffusion limit, and
energy stable under a CFL condition. The derived CFL condition captures the
transition from the hyperbolic to the parabolic regime when approaching the
diffusion limit.
