Y. Wang, W. Bangerth, and J. Ragusa,
"Three-dimensional h-adaptivity for the multigroup neutron diffusion equations,"
Progress in Nuclear Energy
, 51, 543-555 (2009).
Adaptive mesh refinement (AMR) has been shown to allow
solving partial differential equations to significantly higher
accuracy at reduced numerical cost. This paper presents a
state-of-the-art AMR algorithm applied to the multigroup neutron
diffusion equation for reactor applications. In order to follow the
physics closely, energy group-dependent meshes are employed. We
present a novel algorithm for assembling the terms coupling shape
functions from different meshes and show how it can be made
efficient by deriving all meshes from a common coarse mesh by
hierarchic refinement. Our methods are formulated using conforming
finite elements of any order, for any number of energy groups. The
spatial error distribution is assessed with a generalization of an
error estimator originally derived for the Poisson equation.
Our implementation of this algorithm is based on the
widely used Open Source adaptive finite element library deal.II and
is made available as part of this library's extensively documented
tutorial. We illustrate our methods with results for 2-D and 3-D
reactor simulations using 2 and 7 energy groups, and using
conforming finite elements of polynomial degree up to 6.
Associated Project(s):SHIELD (Smuggled HEU Interdiction through Enhanced anaLysis and Detection): A Framework for Developing Novel Detection Systems Focused on Interdicting Shielded HEU