Adaptive smoothing lengths in SPH

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, N, in the range N-NEIB +/- Delta N-NEIB, the tolerance, Delta N-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 N-TOT similar to 6000 particles and N-NEIB = 50. Results. We show that there is a marked reduction in the rates of numerical dissipation and diffusion as. NNEIB 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 NNEIB = 50 and. NNEIB = 10, their results must be viewed with caution.