Modelling the ISM on the grand scale allow us to tackle a set of problems simultaneously, from large to small scales, providing the appropriate grid size, resolution and numerical tools (e.g. adaptive mesh refinement) are used. Among other things global modelling yields information on the formation and lifetimes of molecular clouds, how star-forming regions are determined by large-scale flows in the ISM and whether SNe and superbubbles are important in triggering nearby star formation. In this talk we report on large-scale MHD simulations of the ISM including the disk and Galactic halo using a modified version of the SN driven ISM model of Avillez (2000) coupled to a three-dimensional MHD code that uses adaptive mesh refinement (AMR) in a block-based structure (allowing resolutions as high as 0.625 pc) in combination with Message Passing Interface (MPI) suitable for massive parallel computations. In particular we investigate the role that large scale streams have in the formation of molecular clouds. The modified model includes, among other things, radiative cooling, background heating, and the galactic magnetic field with variable strengths.

  The simulations show that:

    (i) the cold gas is mainly concentrated into filamentary structures,

    (ii) the presence of high density clouds with sizes of a few parsec and having low temperatures,

    (iii) these clouds form and dissipate within some 10-12 Myr being produced by the convergence of large-scale flows,

    (iv) the clouds evolve to high densities over scales of tens of parsecs nearly simultaneously,

    (v) the velocities involved are of the order of the velocity dispersion at the large scales (several km/s), rather than of the internal velocity dispersion of the clouds,

    (vi) cloud build-up time depends on how much mass the streams are carying, how strong the compression is, the rate of cooling of the compressed region and on the geometry of the compression,

    (vii) ram pressure dominates over magnetic and thermal pressures on these clouds, and

    (viii) the mass weighted histograms show that up to 60% of the mass is concentrated in these clouds.