  Numerical models allow the investigation of phenomena that cannot exist in a
laboratory. Computational simulations are therefore essential for advancing our
knowledge of astrophysics, however, the very nature of simulation requires
making assumptions that can substantially affect their outcome. Here, we
present the challenges faced when simulating dim thermonuclear explosions, Type
Iax supernovae. This class of dim events produce a slow moving, sparse ejecta
that presents challenges for simulation. We investigate the limitations of the
equation of state and its applicability to the expanding, cooling ejecta. We
also discuss how the "fluff", i.e. the low-density gas on the grid in lieu of
vacuum, inhibits the ejecta as it expands. We explore how the final state of
the simulation changes as we vary the character of the burning, which
influences the outcome of the explosion. These challenges are applicable to a
wide range of astrophysical simulations, and are important to discuss and
overcome as a community.
