So far our understanding of the evolution of the ISM has beenscanty, because of the inherent nonlinearity of all the processesinvolved. Modelling the interstellar medium in galaxies in aself-consistent way requires an approach that must take into accountthe relevant scales, which may cover several orders of magnitude(e.g., from kpc to less than 1 pc). This is a difficult task thatrequires the use of sophisticated numerical codes, adequatecomputing power, and precision input data from observations. Thelarge range of scales can be resolved by means of adaptive meshrefinement (AMR), that is, the grids reproducing the computationaldomain are refined on the fly such that a minimum number of cells isneeded to provide the most complete description of the flow.
In this paper we review the most recent results on 3D modeling ofthe interstellar medium and disk-halo interaction in a section ofthe Milky Way that includes the Galactic magnetic field, backgroundheating due to starlight, self-gravity and allows for theestablishment of the duty-cycle between the disk and halo (commonlyknown as galactic fountain) by using a grid that extends up to 10kpc on either side of the midplane. Our simulations capture both thelargest structures (e.g., superbubbles) together with the smallerones (e.g., filaments and eddies) down to 0.625 pc. We investigate,among other things, the variability of the magnetic field in theGalactic disk and its correlation with the density, the rôle ofram pressure in the dynamics of disk gas and the relative weight ofthe ram, thermal and magnetic pressures, the mass distribution andthe volume filling factors of the different temperature regimes inthe ISM, as well as the scales at which energy is injected into theinterstellar turbulence and we give an estimate for the dimension ofthe most dissipative structures.