P-1, P-2, AND ASYMPTOTIC APPROXIMATIONS FOR STOCHASTIC TRANSPORT

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.