Homogenization of a neutronic multigroup evolution model

Article type: Research Article

Authors: Capdeboscq, Yves

Affiliations: Department of Math‐Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854‐8019, USA Tel.: +1 732 445 4877; Fax: +1 732 445 5530; E‐mail: ycrc@math.rutgers.edu

Abstract: In this paper is studied the homogenization of an evolution problem for a cooperative system of weakly coupled elliptic partial differential equations, called neutronic multigroup diffusion model, in a periodic heterogenous domain. Such a model is used for studying the evolution of the neutron flux in nuclear reactor core. In this paper, we show that under a symmetry assumption, the oscillatory behavior of the solutions is controled by the first eigenvector of a multigroup eigenvalue problem posed in the periodicity cell, whereas the global trend is asymptotically given by a homogenized evolution problem. We then turn to cases when the symmetry condition is not fulfilled. In domains without boundaries, the limit equation for the global trend is then a homogenized transport equation. Alternatively, we show that in bounded domains and with well prepared initial data, the microscopic scale does not only control the oscillatory behavior of the solutions, but also induces an exponential drift.

Journal: Asymptotic Analysis, vol. 24, no. 2, pp. 143-165, 2000