Spatially Continuous Mixed P2-P1 Solutions for Planar Geometry
P S Brantely · University of North Texas Digital Library (University of North Texas) · 2004
Even-order Legendre polynomial (PN) expansion approximations of the neutron transport equation have historically seen only limited practical application. Research in the last decade [1] has resolved one of the historical theoretical objections [2] to the use of even-order PN approximations in planar geometry, namely the ambiguity in the prescription of boundary conditions as a result of an odd number of unknowns. This research also demonstrated the P2 approximation to be more accurate than the P1 approximation in planar geometry away from boundary layers and material interfaces. Neither the P1 nor the P2 approximation is convincingly more accurate near material interfaces. This progress motivated the reexamination of the multidimensional simplified P2 (SP2) approximation [3], the development of P2 approximations for planar geometry stochastic transport problems [4], and the examination of the P2 and SP2 approximations as a synthetic acceleration technique for the discrete ordinates equations.