Some materials-related microstructural problems calculated using the phase-field method are presented. It is well known that the phase field method requires mesh resolution of a diffuse interface. This makes the use of mesh adaptivity essential especially for fast evolving interfaces and other transient problems. Complex problems in 3D are also computationally challenging so that parallel computations are considered necessary. In this paper, a parallel adaptive finite element scheme is proposed. The scheme keeps the level of node and edge for 2D and level of node and face for 3D instead of the complete history of refinements to facilitate derefinement. The information is local and exchange of information is minimized and also less memory is used. The parallel adaptive algorithms that run on distributed memory machines are implemented in the numerical simulation of dendritic growth and capillary-driven flows.

Due to the importance of uranium and uranium alloys to national defence and nuclear industrial applications, it is necessary to understand dendrite formation in their solidification structures and to control their microstructures. In this study, a modified cellular automaton model was developed to predict 2-D and 3-D equiaxed dendrite growth in U-Nb alloys. The model takes into account solute diffusion, preferential growth orientation, interface curvature, etc., and the solid fraction increment is calculated using the local level rule method. Using this model, 2-D large-scale and 3-D equiaxed dendrite growth with various crystallographic orientations in the U-5.5Nb alloy were simulated, and the Nb micro-segregation behaviour during solidification was analysed. The simulated results showed reasonable agreement with the as-cast microstructure observed experimentally.