Phase field modeling (PFM) is a well-known technique for simulating microstructural evolution. To model grain growth using PFM, typically each grain is assigned a unique non-conserved order parameter and each order parameter field is evolved in time. Traditional approaches using a one-to-one mapping of grains to order parameters present a challenge when modeling large numbers of grains due to the computational expense of using many order parameters. This problem is exacerbated when using an implicit finite element method (FEM), as the global matrix size is proportional to the number of order parameters. While previous work has developed methods to reduce the number of required variables and thus computational complexity and run time, none of the existing approaches can be applied for an implicit FEM implementation of PFM. Here, we present a modular, dynamic, scalable reassignment algorithm suitable for use in such a system. Polycrystal modeling with grain growth and stress require careful tracking of each grain's position and orientation which is lost when using a reduced order parameter set. The method presented in this paper maintains a unique ID for each grain even after reassignment, to allow the PFM to be tightly coupled to calculations of the stress throughout the polycrystal. Implementation details and comparative results of our approach are presented.

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Nuclear energy is a mature technology with a small carbon footprint. However, work is needed to make current reactor technology more accident tolerant and to allow reactor fuel to be burned in a reactor for longer periods of time. Optimizing the reactor fuel performance is essentially a materials science problem. The current understanding of fuel microstructure have been limited by the difficulty in studying the structure and chemistry of irradiated fuel samples at the mesoscale. Here, we take advantage of recent advances in experimental capabilities to characterize the microstructure in 3D of irradiated mixed oxide (MOX) fuel taken from two radial positions in the fuel pellet. We also reconstruct these microstructures using Idaho National Laboratory's MARMOT code and calculate the impact of microstructure heterogeneities on the effective thermal conductivity using mesoscale heat conduction simulations. The thermal conductivities of both samples are higher than the bulk MOX thermal conductivity because of the formation of metallic precipitates and because we do not currently consider phonon scattering due to defects smaller than the experimental resolution. We also used the results to investigate the accuracy of simple thermal conductivity approximations and equations to convert 2D thermal conductivities to 3D. It was found that these approximations struggle to predict the complex thermal transport interactions between metal precipitates and voids.