Boundary layer analysis in the homogenization of neutron transport equations in a cubic domain

Article type: Research Article

Authors: Bal, Guillaume

Affiliations: Department of Mathematics, Stanford University, Stanford, CA 94305, USA E‐mail: [email protected]

Abstract: The homogenization of neutron transport source problems in a finite domain with periodic structure is considered. It is known that the solution of such problems can be factored asymptotically as the product of two terms. The first one gives the local behavior of the neutron transport and is a solution of a periodic transport equation. The second term contains the large scale fluctuations of the neutron density and is a solution of a homogeneous diffusion equation in finite domain. In this paper we present a detailed analysis of the first‐order correction to the expansion that accounts for the neutron leakage at the boundary of the domain. We study a multi‐dimensional boundary layer equation by considering half‐space problems with heterogeneous boundary conditions and exponentially decaying source terms. Modified boundary conditions are then obtained for the homogeneous diffusion equation.

Keywords: Homogenization, linear transport, boundary layer, half‐space problem

Journal: Asymptotic Analysis, vol. 20, no. 3‐4, pp. 213-239, 1999