Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

TL;DR

This study enhances SPH simulations by incorporating an artificial heat conductivity term with gravity-aware signal velocity, improving stability and accuracy in modeling hydrodynamic instabilities and cosmological structures.

Contribution

It introduces a gravity-compatible artificial heat conductivity term in SPH, analyzes stability with the quartic B-spline kernel, and demonstrates improved results in galaxy cluster simulations.

Findings

Quartic B-spline kernel shows excellent stability properties.

Proper limiting conditions on artificial conductivity prevent unphysical heat diffusion.

SPH results with self-gravity align well with mesh-based codes in galaxy cluster profiles.

Abstract

This paper investigates the hydrodynamic performances of an SPH code incorporating an artificial heat conductivity term in which the adopted signal velocity is applicable when gravity is present. In accordance with previous findings it is shown that the performances of SPH to describe the development of Kelvin-Helmholtz instabilities depend strongly on the consistency of the initial condition set-up and on the leading error in the momentum equation due to incomplete kernel sampling. An error and stability analysis shows that the quartic B-spline kernel (M_5) possesses very good stability properties and we propose its use with a large neighbor number, between ~50 (2D) to ~ 100 (3D), to improve convergence in simulation results without being affected by the so-called clumping instability. SPH simulations of the blob test show that in the regime of strong supersonic flows an appropriate limiting condition, which depends on the Prandtl number, must be imposed on the artificial conductivity SPH coefficients in order to avoid an unphysical amount of heat diffusion. Results from hydrodynamic simulations that include self-gravity show profiles of hydrodynamic variables that are in much better agreement with those produced using mesh-based codes. In particular, the final levels of core entropies in cosmological simulations of galaxy clusters are consistent with those found using AMR codes. Finally, results of the Rayleigh-Taylor instability test demonstrate that in the regime of very subsonic flows the code has still several difficulties in the treatment of hydrodynamic instabilities. These problems being intrinsically due to the way in which in standard SPH gradients are calculated and not to the implementation of the artificial conductivity term.