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