  The development of parallel supercomputers allows today the detailed study of
the collapse and the fragmentation of prestellar cores with increasingly
accurate numerical simulations. Thanks to the advances in sub-millimeter
observations, a wide range of observed initial conditions enable us to study
the different modes of low-mass star formation. The challenge for the
simulations is to reproduce the observational results. Two main numerical
methods, namely AMR and SPH, are widely used to simulate the collapse and the
fragmentation of prestellar cores. We compare here thoroughly these two methods
with numerical resolution requirements deduced from previous studies. Our
physical model is as simple as possible, and consists of an isothermal sphere
rotating around the z-axis. We first study the conservation of angular momentum
as a function of the resolution. Then, we explore a wide range of simulation
parameters to study the fragmentation of prestellar cores. There seems to be a
convergence between the two methods, provided resolution in each case is
sufficient. Resolution criteria adapted to our physical cases, in terms of
resolution per Jeans mass, for an accurate description of the formation of
protostellar cores are deduced from the present study. This convergence is
encouraging for future work in simulations of low-mass star formation,
providing the aforementioned criteria are fulfilled.
