Yaqi Wang, Wolfgang Bangerth, Jean Ragusa
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
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.
Three-dimensional h-adaptivity for the multigroup
neutron diffusion equations
Progress in Nuclear Energy, vol. 51 (2009), pp. 543-555.
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.
Thu Feb 15 22:24:40 MST 2018