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 time-steps 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