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The dynamics of star forming clouds is characterized by random supersonic
motions with very large Reynolds number. In order to gain confidence about
our understanding of the initial conditions for the formation of stars
and circumstellar disks, we must address all the potential problems
undermining the computational simulation of such random flows. I will
discuss four main problems: i) Numerical resolution; ii) Magnetized versus
non-magnetized flows; iii) Effect of numerical schemes; iv) Code validation.
These four issues clearly illustrate that a numerical description of the
earliest phase of star formation is within reach, but still very challenging.
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