RESOLUTION REQUIREMENTS FOR SMOOTHED PARTICLE HYDRODYNAMICS CALCULATIONS WITH SELF-GRAVITY

We determine a new resolution requirement for the smoothed particle hy drodynamics (SPH) numerical method when self-gravity is included, Comp arison calculations between an SPH code and an Eulerian grid code are performed. The calculations are of a computationally demanding molecul ar cloud collapse and fragmentation problem. We demonstrate that the r esults given by the two different hydrodynamic methods are in good agr eement, so long as the minimum resolvable mass in the SPH calculations is always less than the Jeans mass, If this criterion is not satisfie d. SPH may give incorrect results, with the stability of near-Jeans-ma ss clumps depending on the details of how the SPH code is implemented rather than on physical processes, We give examples, from the literatu re, of problems that have been encountered in simulations of star, gal axy and cosmological-structure formation where this resolution require ment is ignored.