4 Predictions
Predictions are given in this section that illustrate the interaction
of a piston generated compactionwavewith an embedded
region of sharply varying porosity. The initial solid volume
fraction of the granular solidwas taken as piecewise constant:
φ0(x) =
_
φL 0 ≤ x ≤ 5 cm,
φR 5 ≤ x ≤ 10 cm. (37)
Again, this simple spatial distribution was chosen so that
the time-dependent evolution of incident, transmitted, and
reflected compaction waves with respect to the embedded
interface, and their dependence on φL, φR, and up, could be
cleanly investigated without the development of overly complex
wave interactions resulting from more spatially varying
distributions.Table 1 summarizes the two broad cases considered
in this work. These cases were, respectively, chosen to
characterize how precompaction and piston speed affect the
interaction of an incident wave with a loosely packed region.
For all simulations, we assumed that the bed was initially stationary