Abstract
Based on the AFEPack adaptive software package, the H-adaptive finite element method was used to solve the three-dimensional phase field model on the Linux platform. The growth of the three-dimensional dendrites in the undercooling melt was simulated numerically, and the effects of different undercooling on three-dimensional dendritic growth were studied. The real growth process of three-dimensional dendritic was reproduced. The dendritic growth pattern that we obtained was consistent with the crystallization theory. In order to verify the reliability of the simulation results, the three-dimensional dendrite tip growth rate and the tip radius were compared with the classical theory and the same conditions under the literature value. The results are compared with those obtained by Jeong et al. and obtained by finite difference method under the same conditions. It is found that the results obtained by H-adaptive finite element method are in agreement with the calculated results obtained by these two methods. It is proved that the H-adaptive finite element method is feasible to simulate the growth of three-dimensional dendrites. The method greatly reduces the computational cost of the phase field model solution and improves the efficiency of the solution.
Highlights
Based on the theory of Ginsburg-landau, the phase field method introduces the sequence parameters with time and position change, and establishes the free energy function
The mathematical problem that needs for constant tracking the solid-liquid interface in the process of numerical simulation can be avoided
The numerical simulation of the threedimensional dendritic phase field method begins with the study of Karma and Rappel
Summary
Based on the theory of Ginsburg-landau, the phase field method introduces the sequence parameters with time and position change, and establishes the free energy function. The numerical simulation of the threedimensional dendritic phase field method begins with the study of Karma and Rappel.. The numerical simulation of the threedimensional dendritic phase field method begins with the study of Karma and Rappel.1 They used the phase field method to prove that the microscopic solvable theory is applicable in the process of three-dimensional dendritic growth, which laid the foundation for the development of three-dimensional quantitative simulation of microstructure. Karma and Rappel analyzed the computational efficiency of the phase field method on the two-dimensional and three-dimensional quantitative simulation of dendritic growth. Through the H-adaptive finite element method, the grid can be dynamically adjusted, we achieved the reduction in the number of grids, saved the CPU time required for the calculation, and provided the possibility for large-scale numerical simulations
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
