Dugan, Kevin (2013-08). Dynamic Adaptive Multimesh Refinement for Coupled Physics Equations Applicable to Nuclear Engineering. Master's Thesis.
The processes studied by nuclear engineers generally include coupled physics phenomena (Thermal-Hydraulics, Neutronics, Material Mechanics, etc.) and modeling such multiphysics processes numerically can be computationally intensive. A way to reduce the computational burden is to use spatial meshes that are optimally suited for a specific solution; such meshes are obtained through a process known as Adaptive Mesh Refinement (AMR). AMR can be especially useful for modeling multiphysics phenomena by allowing each solution component to be computed on an independent mesh (Multimesh AMR). Using AMR on time dependent problems requires the spatial mesh to change in time as the solution changes in time. Current algorithms presented in the literature address this concern by adapting the spatial mesh at every time step, which can be inefficient. This Thesis proposes an algorithm for saving computational resources by using a spatially adapted mesh for multiple time steps, and only adapting the spatial mesh when the solution has changed significantly. This Thesis explores the mechanisms used to determine when and where to spatially adapt for time dependent, coupled physics problems. The algorithm is implemented using the Deal.ii fiinite element library [1, 2], in 2D and 3D, and is tested on a coupled neutronics and heat conduction problem in 2D. The algorithm is shown to perform better than a uniformly refined static mesh and, in some cases, a mesh that is spatially adapted at every time step.