A NECESSARY CONDITION FOR INDIVIDUAL TIME STEPS IN SPH SIMULATIONS

We show that the smoothed particle hydrodynamics (SPH) method, used with individual time steps in the way described in the literature, cannot handle strong explosion problems correctly. In the individual time-step scheme, particles determine their time steps essentially from a local Courant condition. Thus they cannot respond to a strong shock, if the pre-shock timescale is too long compared to the shock timescale. This problem is not severe in SPH simulations of galaxy formation with a temperature cutoff in the cooling function at 10(4) K, while it is very dangerous for simulations in which the multiphase nature of the interstellar medium under 10(4) K is taken into account. A solution for this problem is to introduce a time-step limiter which reduces the time step of a particle if it is too long compared to the time steps of its neighbor particles. Thus this kind of time-step constraint is essential for the correct treatment of explosions in high-resolution SPH simulations with individual time steps.