Numerical Models of the ISM

I review recent results from numerical simulations on the structure and dynamics of the ISM, and attempt to put together a coherent dynamical scenario. In particular, I discuss results on 1) the spatial distribution of the gas components, showing that reasonable agreement between simulations and observations exists, but noting that in most models the components are simply defined as temperature intervals, because distinct thermodynamic phases'' do not arise; 2) some statistical issues of the physical fields, like the dependence of the one-point statistics of the density field on the effective equation of state of the gas, the poor correlation of magnetic strength with density, the energy spectrum in weakly and highly compressible cases, and the one point statistics of the velocity field; 3) the effects of spectroscopic observation on distorting the physical structures and results from synthetic observations of the simulations, and 4) several dynamical and thermodynamical issues, such as the role of the thermal instability in forming and confining clouds, the continuous, rather than abrupt, transition between phases’‘, which in turn may be consequences of the dynamics rather than the agents controlling it, the possibility of short time scales ($\sim$ a few Myr) for molecular cloud formation, and the star-gas connection, mentioning that the models generally exhibit self-propagating star and cluster formation, while the stars may drive the medium- and small-scale gas motions, and that a ``star formation instability’’ may induce chaotic behavior of the star formation rate locally. I conclude with a round-up view, and a discussion of the work needed ahead.