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 numerical analysis of the two methods of finding the neutron multiplication time-constant, λ -the direct iteration and quasi-stationary methods - has been performed. The obtained results of computations demonstrate that the direct iteration method requires almost two times smaller number of iterations to find the λ parameter values than the known Kellogg method. The cost-effectiveness of finding parameter λ with the quasi-stationary method is higher, in terms of memory requirements, in comparison with the relaxation method and, sometimes, provides a certain gain in the number of iterations.

      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.