Quantitative 3D phase field modelling of solidification using next-generation adaptive mesh refinement

Michael Greenwood (Corresponding Author), K. N. Shampur, Nana Ofori-Opoku, Tatu Pinomaa, Lei Wang, Sebastian Gurevich, Nikolas Provatas

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

Abstract

Phase field (PF) models are one of the most popular methods for simulating solidification microstructures due to their fundamental connections to the physics of phase transformations. However, these methods are numerically very stiff due to the multiple length scales in a solidifying material, from the nanoscopic solid-liquid interface, to dendritic structures on the order of hundreds of microns. While this problem can be greatly alleviated by thin-interface analytical treatments of the PF equations, additional numerical methods are required to explore experimentally relevant sample sizes and times scales. It was shown about 18 years ago that the use of dynamic adaptive mesh refinement (AMR) can alleviate this problem by exploiting the simple fact that the majority of the solidification kinetics occur at the solid-liquid interface, which scales with a lower dimensionality than the embedding system itself. AMR methods, together with asymptotic analysis, nowadays provide one of the most efficient numerical strategies for self-consistent quantitative PF modelling of solidification microstructure processes. This paper highlights the latest developments in the AMR technique for 3D modelling of solidification using classical phase field equations. This includes a move away from finite element techniques to faster finite differencing through the use of dynamic mini-meshes which are each associated with each node of a 3D Octree data structure, and distributed MPI parallelism that uses a new communication algorithm to decompose a 3D domain into multiple adaptive meshes that are spawned on separate cores. The numerical technique is discussed, followed by demonstrations of the new AMR algorithm on select benchmark solidification problems, as well as some illustrations of multi-phase modelling using a recently developed multi-order parameter phase field model.

Original languageEnglish
Pages (from-to)153-171
Number of pages19
JournalComputational Materials Science
Volume142
Early online date2018
DOIs
Publication statusPublished - 1 Feb 2018
MoE publication typeA1 Journal article-refereed

Fingerprint

Adaptive Mesh Refinement
Phase Field
Solidification
solidification
Phase-field Equations
Modeling
Phase Field Model
liquid-solid interfaces
mesh
Microstructure
Liquid
Dynamic Mesh
Octree
microstructure
Adaptive Mesh
3D Modeling
Asymptotic analysis
data structures
Multiple Scales
Phase Transformation

Keywords

  • Adaptive meshing
  • Large scale simulation
  • Parallel computing
  • Phase field
  • Solidification
  • ProperTune

Cite this

Greenwood, Michael ; Shampur, K. N. ; Ofori-Opoku, Nana ; Pinomaa, Tatu ; Wang, Lei ; Gurevich, Sebastian ; Provatas, Nikolas. / Quantitative 3D phase field modelling of solidification using next-generation adaptive mesh refinement. In: Computational Materials Science. 2018 ; Vol. 142. pp. 153-171.
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abstract = "Phase field (PF) models are one of the most popular methods for simulating solidification microstructures due to their fundamental connections to the physics of phase transformations. However, these methods are numerically very stiff due to the multiple length scales in a solidifying material, from the nanoscopic solid-liquid interface, to dendritic structures on the order of hundreds of microns. While this problem can be greatly alleviated by thin-interface analytical treatments of the PF equations, additional numerical methods are required to explore experimentally relevant sample sizes and times scales. It was shown about 18 years ago that the use of dynamic adaptive mesh refinement (AMR) can alleviate this problem by exploiting the simple fact that the majority of the solidification kinetics occur at the solid-liquid interface, which scales with a lower dimensionality than the embedding system itself. AMR methods, together with asymptotic analysis, nowadays provide one of the most efficient numerical strategies for self-consistent quantitative PF modelling of solidification microstructure processes. This paper highlights the latest developments in the AMR technique for 3D modelling of solidification using classical phase field equations. This includes a move away from finite element techniques to faster finite differencing through the use of dynamic mini-meshes which are each associated with each node of a 3D Octree data structure, and distributed MPI parallelism that uses a new communication algorithm to decompose a 3D domain into multiple adaptive meshes that are spawned on separate cores. The numerical technique is discussed, followed by demonstrations of the new AMR algorithm on select benchmark solidification problems, as well as some illustrations of multi-phase modelling using a recently developed multi-order parameter phase field model.",
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Quantitative 3D phase field modelling of solidification using next-generation adaptive mesh refinement. / Greenwood, Michael (Corresponding Author); Shampur, K. N.; Ofori-Opoku, Nana; Pinomaa, Tatu; Wang, Lei; Gurevich, Sebastian; Provatas, Nikolas.

In: Computational Materials Science, Vol. 142, 01.02.2018, p. 153-171.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Shampur, K. N.

AU - Ofori-Opoku, Nana

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AU - Gurevich, Sebastian

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