An implicit parallel multigrid computing scheme to solve coupled thermal-solute phase-field equations for dendrite evolution

Guo, Z.; Mi, J.; Grant, P. S.

Abstract

An implicit, second-order space and time discretization scheme together with a parallel multigrid method involving a strip grid domain partitioning has been developed to solve fully coupled, nonlinear phase field equations involving solute and heat transport for multiple solidifying dendrites. The computational algorithm has been shown to be stable and monotonously convergent, and allowed time marching steps that were 3–4 orders of magnitude larger than those employed in similar explicit approaches, resulting in an increase of 3–4 orders of magnitude in computing efficiency. Full solute and thermal coupling was achieved for metallic alloys with a realistic, high Lewis number of >104. The parallel multigrid computing scheme is shown to provide a scalable methodology that allowed the efficient use of distributed supercomputing resource to simulate the evolution of tens of complex shaped 2D dendrites in a computational domain containing tens or even hundreds of millions of grid points. The simulations have provided insight into the dynamic interplay of many growing dendrites in a more realistic fully coupled thermal-solute condition, capturing for the first time fine scale features such as dendrite splitting.

Citation

Guo, Z., Mi, J., & Grant, P. S. (2012). An implicit parallel multigrid computing scheme to solve coupled thermal-solute phase-field equations for dendrite evolution. Journal of Computational Physics, 231(4), 1781-1796. https://doi.org/10.1016/j.jcp.2011.11.006

• Journal Article Type: Article
• Acceptance Date: Nov 5, 2011
• Online Publication Date: Nov 16, 2011
• Publication Date: Feb 20, 2012
• Deposit Date: Nov 13, 2014
• Journal: Journal Of Computational Physics
• Print ISSN: 0021-9991
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 231
• Issue: 4
• Pages: 1781-1796
• DOI: https://doi.org/10.1016/j.jcp.2011.11.006
• Keywords: Physics and Astronomy (miscellaneous); Computer Science Applications
• Public URL: https://hull-repository.worktribe.com/output/467736
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0021999111006486?via%3Dihub
• Contract Date: Nov 13, 2014