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Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method for solving thefluid equations that is commonplace in astrophysics, prized for its naturaladaptivity and stability. The choice of variable to smooth in SPH has been thetopic of contention, with smoothed pressure (P-SPH) being introduced to reduceerrors at contact discontinuities relative to smoothed density schemes.Smoothed pressure schemes produce excellent results in isolated hydrodynamicstests; in more complex situations however, especially when coupling to the`sub-grid' physics and multiple time-stepping used in many state-of-the-artastrophysics simulations, these schemes produce large force errors that caneasily evade detection as they do not manifest as energy non-conservation. Heretwo scenarios are evaluated: the injection of energy into the fluid (common forstellar feedback) and radiative cooling. In the former scenario, force andenergy conservation errors manifest (of the same order as the injected energy),and in the latter large force errors that change rapidly over a few timestepslead to instability in the fluid (of the same order as the energy lost tocooling). Potential ways to remedy these issues are explored with solutionsgenerally leading to large increases in computational cost. Schemes using aDensity-based formulation do not create these instabilities and as such it isrecommended that they are preferred over Pressure-based solutions when combinedwith an energy diffusion term to reduce errors at contact discontinuities.

Inconsistencies arising from the coupling of galaxy formation sub-grid models to Pressure-Smoothed Particle Hydrodynamics