  Dealing numerically with the turbulent nature and non-linearity of the
physical processes involved in the ISM requires the use of sophisticated
numerical schemes coupled to HD and MHD mathematical models. SNe are the main
drivers of the interstellar turbulence by transferring kinetic energy into the
system. This energy is dissipated by shocks (which is more efficient) and by
molecular viscosity. We carried out adaptive mesh refinement simulations (with
a finest resolution of 0.625 pc) of the turbulent ISM embedded in a magnetic
field with mean field components of 2 and 3 $\mu$G. The time scale of our run
was 400 Myr, sufficiently long to avoid memory effects of the initial setup,
and to allow for a global dynamical equilibrium to be reached in case of a
constant energy input rate. It is found that the longitudinal and transverse
turbulent length scales have a time averaged (over a period of 50 Myr) ratio of
0.52-0.6, almost similar to the one expected for isotropic homogeneous
turbulence. The mean characteristic size of the larger eddies is found to be
\~75 pc in both runs. In order to check the simulations against observations,
we monitored the OVI and HI column densities within a superbubble created by
the explosions of 19 SNe having masses and velocities of the stars that
exploded in vicinity of the Sun generating the Local Bubble. The model
reproduces the FUSE absorption measurements towards 25 white dwarfs of the \ovi
column density as function of distance and of \nhi. In particular for lines of
sight with lengths smaller than 120 pc it is found that there is no correlation
between N(OVI) and N(HI).
