  We elucidate the interplay between Newtonian thermal relaxation and numerical
dissipation, of several different origins, in flow simulations of hot
extrasolar planet atmospheres. Currently, a large range of Newtonian
relaxation, or "cooling", times (~10 days to ~1 hour) is used among different
models and within a single model over the model domain. In this study we
demonstrate that a short relaxation time (much less than the planetary rotation
time) leads to a large amount of unphysical, grid-scale oscillations that
contaminate the flow field. These oscillations force the use of an excessive
amount of artificial viscosity to quench them and prevent the simulation from
"blowing up". Even if the blow-up is prevented, such simulations can be highly
inaccurate because they are either severely over-dissipated or
under-dissipated, and are best discarded in these cases. Other numerical
stability and timestep size enhancers (e.g., Robert-Asselin filter or
semi-implicit time-marching schemes) also produce similar, but less excessive,
damping. We present diagnostics procedures to choose the "optimal" simulation
and discuss implications of our findings for modeling hot extrasolar planet
atmospheres.
