AN IMPROVED P₀-TRANSPORT APPROXIMATION USED TO DESCRIBE THE ANGULAR DISTRIBUTION OF NEUTRONS IN INTERGROUP TRANSITIONS DUE TO SCATTERING

V.P. Gorelov, Yu.V. Petrov, G.G. Farafontov
VANT. Ser.: Mat. Mod. Fiz. Rroc 1990. Вып.2. С. 30-34.

      The paper suggests three forms of approximately describing the angular distribution of neutrons in transitions between groups due to neutron scattering. The first of them called the P₀-transport approximation is preferable for application in practice. It allows reducing the collision integral of the transport equation written for a 2D, or a 3D region to the single one with the D₂-approximation characteristics being preserved and the collision integral positivity being ensured, in contrast to the latter.

      The paper suggests an approach to solving a system of ordinary differential equations, which are the result of S_N- or DS_N- transformations applied to the equation of neutron transport in a solid sphere. The procedure of accelerating successive approximations without any significant increase of the amount of computations is described. The approach discussed in the paper is not associated with the use of the original equations in their finite difference form and reduced to the use of step-by-step methods (Runge-Kutta, predictor-corrector, etc.) of solving problems with the specified initial conditions.

      The paper suggests the transformation simplifying the multigroup neutron transport equation corresponding to the use of the P₀-transport approximation when describing the angular neutron distribution in transitions between groups due to scattering. The transformation is called “modal” and allows writing the transport equation in the form corresponding to the assumed isotropic angular distribution of scattered neutrons. The specific features of using the modal transformation in problems with sources and in problems of finding various eigenvalues are discussed.