Adaptive smoothing lengths in SPH

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, , in the range , the tolerance, , 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 particles and .

Results.We show that there is a marked reduction in the rates of numerical dissipation and diffusion as 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 and , their results must be viewed with caution.