The problem of describing particle transport through a Markovian stoch
astic mixture of two immiscible materials is generally approximated by
the so-called Levermore model, consisting of two coupled transport eq
uations. In this paper, the P-2 diffusive equations and the associated
boundary conditions for this Levermore model are derived in planar ge
ometry by using a variational principle, and numerical results compari
ng P-2, P-1, and S-16 (benchmark) calculations are presented. These re
sults demonstrate that the P-2 equations are considerably more accurat
e than the P-1 equations away from boundary layers. An asymptotic diff
usion approximation to this model is also explored with several differ
ent boundary conditions, and the overall conclusion is that the asympt
otic diffusion treatment is in general inferior to P-2 theory, and its
superiority over P-1 theory is not overwhelming and not consistent.