Simulation And Research Of The Phase-field Model Based On Adaptive Finite Element Method

Whether in the pure substance supercooled melt or alloy, dendrite is a kind of typical and common microstructure morphology. Phase field model is a kind of numerical simulation method that can simulate evolution mechanism of the complex interface during the process of dendrite growth well. However, the conventional numerical calculation method based on uniform grid has a huge amount of computation and poor efficiency in solving phase-field model. In addition, with the deepening of the research,the established phase model become more and more complex which makes it almost a impossible task adopting traditional numerical calculation method to solve the phase field model for single computer. Numerical calculation method also needs to be constantly optimized. Therefore, this thesis employs the high efficiency adaptive finite element method to solve the phase field model. Based on this research interest, this thesis is consist of the following aspects:(1) Firstly, the basic theory of the finite element method is introduced. In fact, the nature of the phase field model is partial differential equation, it must be transformed into the corresponding weak form before solving the phase field model with the finite element method. The general transformation process from partial differential equations to corresponding weak form is explained. Secondly, this thesis introduced the compile installation process of the adaptive finite element function library AFEPack, addressed the problems during the process of compiling and established the environment for adaptive finite element to solve the phase field model.(2) Wheeler’s pure substance phase-field model are adopted in this article. The adaptive finite element based on non-uniform grids are employed to solve phase-field model. The influence of different larger computional domain on the dendrite tip velocity and the influence of different thermal noise intensity on dendrite morphology are studied. The results show that larger different calculation domains have little effects on the balance value of the dendrite tip velocity. With the increase of fluctuation intensity, The dendrite tips obtain a higher temperature gradient and isothermal curves fluctuates dramatically that lead to the primary arms lose stability and the numbers of secondary arms become larger and larger. In addition,the adaptive finite element method can reduce CPU time consuming and the necessary nodes by one order of magnitude compared with uniform grid approach and the speedup is proportional to the system size. The larger system size, the better reflect superiority of adaptive finite element method.(3) Projection algorithm and adaptive finite element method is employed respectively to solve the equation of flow field and phase field. Simulation results show that when the flow velocity is less than the threshold value, the asymmetry of dendrite has been less affected by convection. Once the flow velocity reaches or exceeds the value, thermal conductivity of the controlling factors gradually transform from thermal diffusion to convection. Along with the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem become larger and larger. The vortex region of dendrite tip is gradual enlargement and remelted.