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A Modified P3-Like Approximation to the Transport Equation

Bingjing Su, G. C. Pomraning

Nuclear Science and Engineering / Volume 124 / Number 2 / October 1996 / Pages 309-319

Technical Paper /

Standard PN theory is well developed as an approximation to the neutron transport equation. However, this theory contains no physics in the sense that it simply represents the angular flux as a sum of polynomials in angle. Thus, standard PN theory (with N finite) cannot qualitatively predict correct asymptotic transport behavior except in the limit of pure scattering. In this paper‚ we modify standard PN theory by incorporating certain transport physics, namely, the Case discrete modes, into a modified PN expansion of the angular flux. The theory resulting from using this modified PN-like expansion predicts the exact transport asymptotic growth/decay length, since it contains the discrete Case eigenvalue. Such modified P3-like equations and associated boundary conditions are derived in planar geometry according to a recently introduced variational calculus. Analyses and numerical calculations reveal that this modified P3-like theory possesses the following features: (a) It reduces to standard P3 theory in the limit of pure scattering; (b) it conserves neutrons but exhibits a scalar flux discontinuity at a material interface; (c) it is shown numerically to be exceedingly accurate, much more accurate than standard P3 theory, in predicting various transport theory behavior for homogeneous problems; and (d) for heterogeneous problems, it is necessary that each material region in the system be sufficiently large for this theory to predict better results than standard P3 theory.