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.