  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 muG).
