Spatially adaptive eigenvalue estimation for the SN equations on unstructured triangular meshes

Highlights: → We investigate spatial adaptivity for the multiplication eigenvalue of the SN equations. → The method is based on the use an adjoint weighted error measure. → The algorithm is applied to unstructured triangular meshes. → The resulting algorithm is efficient in terms of number of elements required compared to uniform refinement. - Abstract: Adaptive mesh refinement is a powerful method for efficiently solving physical problems described by partial differential equations at reduced computational cost. In this paper we present a new adaptive algorithm for estimating the effective multiplication factor, keff, for the neutron transport equation. The method is based on a dual weighted residual approach where an appropriate adjoint problem is solved to obtain the importance of residual errors to the multiplication factor. The forward residuals and the importance are then combined to give accurate error measures which are used to design economical finite element meshes. We illustrate the effectiveness of our methods by applying them to two 2-dimensional reactor problems by comparing the quality of the error estimator which is the basis for adaptivity and the overall efficiency which is judged by the number of elements required for a given accuracy.