  Supernova (SN) blast waves inject energy and momentum into the interstellar
medium (ISM), control its turbulent multiphase structure and the launching of
galactic outflows. Accurate modelling of the blast wave evolution is therefore
essential for ISM and galaxy formation simulations. We present an efficient
method to compute the input of momentum, thermal energy, and the velocity
distribution of the shock-accelerated gas for ambient media with uniform (and
with stellar wind blown bubbles), power-law, and turbulent density
distributions. Assuming solar metallicity cooling, the blast wave evolution is
followed to the beginning of the momentum conserving snowplough phase. The
model recovers previous results for uniform ambient media. The momentum
injection in wind-blown bubbles depend on the swept-up mass and the efficiency
of cooling, when the blast wave hits the wind shell. For power-law density
distributions with $n(r) \sim$ $r^{-2}$ (for $n(r) > n_{_{\rm floor}}$) the
amount of momentum injection is solely regulated by the background density
$n_{_{\rm floor}}$ and compares to $n_{_{\rm uni}}$ = $n_{_{\rm floor}}$.
However, in turbulent ambient media with log-normal density distributions the
momentum input can increase by a factor of 2 (compared to the homogeneous case)
for high Mach numbers. The average momentum boost can be approximated as
$p_{_{\rm turb}}/\mathrm{p_{_{0}}}\ =23.07\, \left(\frac{n_{_{0,\rm
turb}}}{1\,{\rm cm}^{-3}}\right)^{-0.12} + 0.82
(\ln(1+b^{2}\mathcal{M}^{2}))^{1.49}\left(\frac{n_{_{0,\rm turb}}}{1\,{\rm
cm}^{-3}}\right)^{-1.6}$. The velocity distributions are broad as gas can be
accelerated to high velocities in low-density channels. The model values agree
with results from recent, computationally expensive, three-dimensional
simulations of SN explosions in turbulent media.
