Numerical simulations of the multi-phase interstellar medium have been carried out , using a 3D , nonlinear , magnetohydrodynamic , shearing-box model , with random motions driven by supernova explosions .
These calculations incorporate the effects of magnetic fields and rotation in 3D ; these play important dynamical roles in the galaxy , but are neglected in many other simulations .
The supernovae driving the motions are not arbitrarily imposed , but occur where gas accumulates into cold , dense clouds ; their implementation uses a physically motivated model for the evolution of such clouds .
The process is self-regulating , and produces mean supernova rates as part of the solution .
Simulations with differing mean density show a power law relation between the supernova rate and density , with exponent 1.7 ; this value is within the range suggested from observations ( taking star formation rate as a proxy for supernova rate ) .
The global structure of the supernova driven medium is strongly affected by the presence of magnetic fields ; e.g .
for one solution the filling factor of hot gas is found to vary from 0.19 ( with no field ) to 0.12 ( with initial mid-plane field B _ { 0 } = 6 \mu { G } ) .