Inconsistencies arising from the coupling of galaxy formation sub-grid
  models to Pressure-Smoothed Particle Hydrodynamics
  Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method for solving the
fluid equations that is commonplace in astrophysics, prized for its natural
adaptivity and stability. The choice of variable to smooth in SPH has been the
topic of contention, with smoothed pressure (P-SPH) being introduced to reduce
errors at contact discontinuities relative to smoothed density schemes.
Smoothed pressure schemes produce excellent results in isolated hydrodynamics
tests; in more complex situations however, especially when coupling to the
`sub-grid' physics and multiple time-stepping used in many state-of-the-art
astrophysics simulations, these schemes produce large force errors that can
easily evade detection as they do not manifest as energy non-conservation. Here
two scenarios are evaluated: the injection of energy into the fluid (common for
stellar feedback) and radiative cooling. In the former scenario, force and
energy conservation errors manifest (of the same order as the injected energy),
and in the latter large force errors that change rapidly over a few timesteps
lead to instability in the fluid (of the same order as the energy lost to
cooling). Potential ways to remedy these issues are explored with solutions
generally leading to large increases in computational cost. Schemes using a
Density-based formulation do not create these instabilities and as such it is
recommended that they are preferred over Pressure-based solutions when combined
with an energy diffusion term to reduce errors at contact discontinuities.
