  The effect of gas compression at the developed stages of flame acceleration
in smooth-wall and obstructed channels is studied. We demonstrate analytically
that gas compression moderates the acceleration rate and perform numerical
simulations within the problem of flame transition to detonation. It is shown
that flame acceleration undergoes three distinctive stages: 1) initial
exponential acceleration in the incompressible regime, 2) moderation of the
acceleration process due to gas compression, so that the exponential
acceleration state goes over to a much slower one, 3) eventual saturation to a
steady (or statistically-steady) high-speed deflagration velocity, which may be
correlated with the Chapman-Jouguet deflagration speed. The possibility of
deflagration-to-detonation transition is demonstrated.
