Phase Field Simulation Of Solidification Behaviors In Undercooled Melts Using Adaptive Fem

The phase-field model as a method of quantitatively simulating solidification microstructures emerged in recent years. Due to several scales ranging from 10^-9m to 10^-3m are involved during the physical processes of solidification, the numerical simulation for the phase field model is extraordinary time consuming, which greatly limits its application to the simulation of solidification microstructures. So how to reduce the capacity of computation and memory and extend solvable dimensions comes into being the main problem. At the same time, it has been established by theory and experiments that the solid/liquid interface anisotropy has profound effects on the growth pattern selection of crystallization, but it was still yet lack of quantitative investigation impeded by the great difficulty in mathematical analysis and experiments.Based on the construction of a reliable, efficient algorithm - adaptive finite element method (AFEM) - for solving the phase-field equations, the crystal growth in the undercooled melts is quantitatively simulated. And the main factors such as undercooling, anisotropy of interfacial energy and kinetics have been discussed extensively. The main research work and conclusions are as follows:1. The generation method of efficient dynamic adaptive mesh is proposed. The Zienkiewicz-Zhu method is used to estimate the error of elements, meanwhile, the method of mass lumping together with a composite field ψ are adopted to reduce the computation consumption for the error estimation. The generation algorithm of adaptive mesh which is based on the quad-tree data structure is presented. With this algorithm, the computation time is reduced from N_u～L³ in uniform grids to N_a～L² and the capacity of memory requirement is reduced from M_u～L² to M_a～L.2. According to the feature of the adaptive mesh, an efficient algorithm for the MSR data structure generation is proposed. The ICCG and GMRES solver for the large-scale linear system of equations is formulated.3. The dependence of mesh anisotropy on â–³x/W₀ and R₀ is scaled. This anisotropy increases with â–³x/W₀ but independent of R₀; it could be omitted when ε₄>0.03 but should be considered under the low anisotropy.4. The effect of interface energy anisotropy on growth is investigated. The velocity...