  Detonation propagation in a compressible medium wherein the energy release
has been made spatially inhomogeneous is examined via numerical simulation. The
inhomogeneity is introduced via step functions in the reaction progress
variable, with the local value of energy release correspondingly increased so
as to maintain the same average energy density in the medium, and thus a
constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate
governs the rate of energy release in the reactive zones. The resulting
dynamics of a detonation propagating in such systems with one-dimensional
layers and two-dimensional squares are simulated using a Godunov-type
finite-volume scheme. The resulting wave dynamics are analyzed by computing the
average wave velocity and one-dimensional averaged wave structure. In the case
of sufficiently inhomogeneous media wherein the spacing between reactive zones
is greater than the inherent reaction zone length, average wave speeds
significantly greater than the corresponding CJ speed of the homogenized medium
are obtained. If the shock transit time between reactive zones is less than the
reaction time scale, then the classical CJ detonation velocity is recovered.
The spatio-temporal averaged structure of the waves in these systems is
analyzed via a Favre averaging technique, with terms associated with the
thermal and mechanical fluctuations being explicitly computed. The analysis of
the averaged wave structure identifies the super-CJ detonations as weak
detonations owing to the existence of mechanical non-equilibrium at the
effective sonic point embedded within the wave structure. The correspondence of
the super-CJ behavior identified in this study with real detonation phenomena
that may be observed in experiments is discussed.
