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

Abstract

This paper investigates the hydrodynamic performances of an smoothed particle hydrodynamics (SPH) code incorporating an artificial heat conductivity term in which the adopted signal velocity is applicable when gravity is present. To this end, we analyze results from simulations produced using a suite of standard hydrodynamical test problems. In accordance with previous findings, we show that the performances of SPH in describing the development of Kelvin-Helmholtz instabilities depend strongly on both the consistency of the initial condition set-up and the leading error in the momentum equation due to incomplete kernel sampling. In contrast, the presence of artificial conductivity does not significantly affect the results. An error and stability analysis shows that the quartic B-spline kernel (M 5 ) possesses very good stability properties and so 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. Moreover, the results of the Sod shock tube demonstrate that to obtain simulation profiles in accord with the analytic solution, for simulations employing kernels with a non-zero first derivative at the origin, it is necessary to use a much larger number of neighbors than in the case of the M 5 runs. Our SPH simulations of the blob test show that in order to achieve blob disruption it is necessary to include an artificial conductivity term. However, we find 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. Our 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. This demonstrates that the proposed diffusion scheme is capable of mimicking the process of entropy mixing that is produced during structure formation because of the diffusion caused by turbulence. Finally, the results of our Rayleigh-Taylor instability test demonstrate that in the regime of very subsonic flows the code still has several difficulties in the treatment of hydrodynamic instabilities. These problems are intrinsic to the way in which standard SPH gradients are calculated and not to the implementation of the artificial conductivity term. To overcome these difficulties, several numerical schemes have been proposed that, if coupled with the SPH implementation presented in this paper, could solve the issues that have recently been addressed in investigating SPH performances to model subsonic turbulence.

Improved Performances in Subsonic Flows of an SPH Scheme With Gradients Estimated Using an Integral Approach

“…In the low Mach number regime the difficulties of standard SPH have been found to be particularly severe (Bauer & Springel 2012;Dehnen & Aly 2012;García-Senz et al 2012;McNally et al 2012;Valdarnini 2012;Hopkins 2015) and gradient accuracy is a key prerequisite for accurate modeling the fluid dynamics.…”

“…The KH instability has been investigated by many authors since it is a classic test in which SPH fails to properly model the development of the instability (Price 2008;Read et al 2010;Valcke et al 2010;Junk et al 2010;Heß & Springel 2010;Cha et al 2010;Murante et al 2011;Valdarnini 2012;McNally et al 2012;Kawata et al 2014;Hu et al 2014;Hopkins 2015).…”

The role of the artificial conductivity in SPH simulations of galaxy clusters: effects on the ICM properties

“…This choice guarantees the absence of thermal diffusion for self-gravitating systems in hydrostatic equilibrium and its reliability has been tested in a number of hydrodynamical tests (Valdarnini 2012) in which gravity is present. Finally, for the cooling runs, the term QR = −Λ(ρi, Ti) -Ti being the particle temperature -accounts for the radiative losses.…”

“…For instance, being the method Lagrangian, it has very good conservation properties and, moreover, is naturally adaptive. For this reason, many authors have recently proposed several improvements in the numerical scheme to solve the problems encountered by standard SPH in handling fluid instabilities (Price 2008;Cha et al 2010;Heß & Springel 2010;Abell 2011;Murante et al 2011;Read & Hayfield 2012;García-Senz et al 2012;Valdarnini 2012;Power et al 2014;Saitoh & Makino 2013;Hu et al 2014;Hopkins 2014). In particular, Price (2008) suggested to include in the SPH thermal energy equation an artificial conduction (AC) term with the purpose of smoothing the thermal energy at fluid interfaces and in turn to ensure a smooth entropy transition at contact discontinuities.…”

“…A similar term was introduced by Wadsley et al (2008) with the aim of mimicking the effects of turbulence diffusion, which in SPH is inhibited by the Lagrangian nature of the method. The hydrodynamical performances of this approach were later investigated in detail (Valdarnini 2012), indicating a general improvement over standard SPH in a number of hydrodynamical test problems. In particular, the final levels of core entropies in cosmological simulations of galaxy clusters were found consistent with those found using AMR codes.…”