Adaptive smoothing lengths in SPH

Free access article

Issue		A&A Volume 464, Number 2, March III 2007


Page(s)		447 - 450
Section		Astrophysical processes
DOI		http://dx.doi.org/10.1051/0004-6361:20066606

A&A 464, 447-450 (2007)
DOI: 10.1051/0004-6361:20066606

Adaptive smoothing lengths in SPH

R. E. Attwood¹, S. P. Goodwin², and A. P. Whitworth¹

¹ School of Physics & Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, Wales, UK
e-mail: [Rhianne.Attwood; Anthony.Whitworth]@astro.cf.ac.uk
² Department of Physics & Astronomy, University of Sheffield, Hicks Building, Housfield Road, Sheffield S3 7RH, UK
e-mail: S.Goodwin@Sheffield.ac.uk

(Received 20 October 2006 / Accepted 18 December 2006 )

Abstract
Context.There is a need to improve the fidelity of SPH simulations of self-gravitating gas dynamics.
Aims.We remind users of SPH that, if smoothing lengths are adjusted so as to keep the number of neighbours, ${\cal N}$ , in the range ${\cal N}_{{\rm NEIB}}\pm\Delta{\cal N}_{{\rm NEIB}}$ , the tolerance, $\Delta{\cal N}_{{\rm NEIB}}$ , should be set to zero, as first noted by Nelson & Papaloizou. We point out that this is a very straightforward and computationally inexpensive constraint to implement.
Methods.We demonstrate this by simulating acoustic oscillations of a self-gravitating isentropic monatomic gas-sphere (cf. Lucy), using ${\cal N}_{{\rm TOT}}\sim6000$ particles and ${\cal N}_{{\rm NEIB}}=50$ .
Results.We show that there is a marked reduction in the rates of numerical dissipation and diffusion as $\Delta{\cal N}_{{\rm NEIB}}$ is reduced from 10 to zero. Moreover this reduction incurs a very small computational overhead.
Conclusions.We propose that this should become a standard test for codes used in simulating star formation. It is a highly relevant test, because pressure waves generated by the switch from approximate isothermality to approximate adiabaticity play a critical role in the fragmentation of collapsing prestellar cores. Since many SPH simulations in the literature use ${\cal N}_{{\rm NEIB}}=50$ and $\Delta{\cal N}_{{\rm NEIB}}\geq10$ , their results must be viewed with caution.

Key words: hydrodynamics -- methods: numerical -- stars: oscillations

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