Inconsistencies arising from the coupling of galaxy formation sub-grid models to pressure-smoothed particle hydrodynamics

Abstract

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.

Osaka Feedback Model. II. Modeling Supernova Feedback Based on High-resolution Simulations

“…When thermal FB injects energy, updating the entropy assuming a fixed pressure leads to the wrong result because the smoothed pressure field itself depends on the entropy. Therefore, we use an iterative method to calculate the entropy change by an energy injection from the FB and energy dissipation by radiative cooling (Schaye et al 2015;Borrow et al 2021). The self-gravity of SPH and collisionless particles are also considered.…”

The importance of black hole repositioning for galaxy formation simulations

“…, where only a maximum fraction of 0.3 𝑁 ngb was targeted for heating in any one time step to avoid energy conservation violations in the pressure-entropy formulation of hydrodynamics used there (see appendix A1.1 of Schaye et al 2015). The density-energy based hydrodynamics scheme that we use is explicitly designed and tested to not require such a limitation (Borrow et al , 2021.…”

Osaka Feedback Model II: Modeling Supernova Feedback Based on High-Resolution Simulations

“…When thermal feedback injects energy, updating entropy assuming fixed pressure leads to the wrong result because the smoothed pressure field itself depends on the entropy. Therefore, we use an iterative method to calculate entropy change by energy injection from feedback and energy dissipation by radiative cooling (Schaye et al 2015;Borrow et al 2021). The self-gravity of SPH and collisionless particles are also considered.…”