VARIATIONAL DERIVATION AND NUMERICAL-ANALYSIS OF P2 THEORY IN PLANAR GEOMETRY

Even-order P(N) theory has historically been viewed as a questionable approximation to transport theory. The main reason is that one obtains an odd number of unknowns and equations; this causes an ambiguity in the prescription of boundary conditions. We derive the one-group plana r-geometry P2 equations and associated boundary conditions using a sim ple, physically motivated variational principle. We also present numer ical results comparing P2, P1, and SN calculations. These results demo nstrate that for most problems, the P2 equations with variational boun dary conditions are considerably more accurate than the P1 equations w ith either the Marshak or the Federighi-Pomraning boundary conditions (both of which have also been derived variationally). Moreover, becaus e the P2 and P1 equations can be written in diffusion form, the discre tized P2 equations require nearly the same computational effort to sol ve as the discretized P1 equations. Our variational method can easily be extended to higher even-order P(N) approximations.