Development of a parallel adaptive multigrid algorithm for solving the multi-scale thermal-solute 3D phase-field problems - Wu, Jun; Guo, Zhipeng; Luo, Chao (Computational materials science, 2018)
[Display omitted] A parallel adaptive multigrid algorithm was developed to solve the coupled thermal-solute phase field equations so that the multi-scale difficulty of the problem when both thermal and solute fields were presented could be resolved. Comparing with the explicit method, it was showed that the proposed algorithm even converged when the time step was enlarged to be 4 orders of magnitude larger, and combined with Para-AMR algorithm [1] the computation efficiency could be improved by about 4–5 orders of magnitude with little accuracy compromised, when a much higher and realistic Lewis number was used, e.g. Le=10,000. With this numerical capability, 3D phase field simulations on dendrite growth in a much larger scale, in particular under multi-scale thermal-solute conditions, could be performed in a much more sensible manner with moderate amount of computing resources. Dendrite growth simulations with Le varying from 1 to 10,000 in 3D were carried out for the first time, and the result showed that variation of Le led to a great difference of both tip velocity and tip radius, which was similar to the 2D case reported by [2].