An arbitrary geometry finite element method for the adjoint neutron transport equation

Abstract

In this paper a variational formulation for the adjoint even parity neutron transport equation (NTE) based on the generalized least squares method is adopted. The so-called PN method or expansion via Spherical Harmonics Polynomials (SHPs) is then summoned to treat the angular dependency of the equation while Finite Element Method (FEM) is invoked for the spatial domain. Based on our matrix form approach, it is shown that the scalar adjoint flux, ϕ†(r), can be determined through an efficient approach solely or in parallel with the scalar forward flux, ϕ(r). Eigenvalue problems as well as detector readings are of most useful applications of the adjoint calculation which are also discussed in this survey. To verify the equations we upgraded our Even parity Neutron TRANSport code, ENTRANS, with an adjoint solver which is capable of handling one-, two- and three-dimensional problems of arbitrary geometry. Ability to cover any order of multigroup scattering anisotropy (with or without up-scattering) as well as higher order elements is also embedded in the ENTRANS. Finally, several test cases are examined against reference results to illustrate the accuracy and efficiency of the proposed approach.