A Review of Neutron Transport Approximations

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Abstract
Numerical methods for solving the integrodifferential, integral, and surface-integral forms of the neutron transport equation are reviewed. The solution methods are shown to evolve from only a few basic numerical approximations, such as expansion techniques or the use of quadrature formulas. The emphasis is on the derivation of the approximate equations from the transport equation, and not on the solution of the resulting system of algebraic equations. The presentation covers the approaches used in general-purpose production calculations, including the discrete ordinates finite difference method, the method of characteristics, finite element approximations, the collision-probability method, and nodal methods. Various quasi-analytical techniques for calculating benchmark problems are also treated, such as the singular eigenfunction, spherical harmonics, integral transform, and CN and FN methods.

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