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 \sim 75 pc in both runs .
In order to check the simulations against observations , we monitored the O vi and H i 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 O vi column density as function of distance and of N ( H i ) .
In particular for lines of sight with lengths smaller than 120 pc it is found that there is no correlation between N ( O vi ) and N ( H i ) .