A more accurate two-dimensional grain growth algorithm

Emanuel A. Lazar; Robert D. MacPherson; David J. Srolovitz

doi:10.1016/j.actamat.2009.09.008

A more accurate two-dimensional grain growth algorithm

Emanuel A. Lazar, Robert D. MacPherson, David J. Srolovitz

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

We describe a method for evolving two-dimensional polycrystalline microstructures via mean curvature flow that satisfies the von Neumann-Mullins relation with an absolute error O (Δ t²). This is a significant improvement over a different method currently used that has an absolute error O (Δ t). We describe the implementation of this method and show that while both approaches lead to indistinguishable evolution when the spatial discretization is very fine, the differences can be substantial when the discretization is left unrefined. We demonstrate that this new front-tracking approach can be pushed to the limit in which the only mesh nodes are those coincident with triple junctions. This reduces the method to a vertex model that is consistent with the exact kinetic law for grain growth. We briefly discuss an extension of the method to higher spatial dimensions.

Original language	English
Pages (from-to)	364-372
Number of pages	9
Journal	Acta Materialia
Volume	58
Issue number	2
DOIs	https://doi.org/10.1016/j.actamat.2009.09.008
State	Published - Jan 2010
Externally published	Yes

Bibliographical note

Funding Information:
The authors gratefully acknowledge the support of the DARPA Defense Sciences office; EAL also thanks the US Department of Defense for an NDSEG fellowship. The authors would also like to thank the anonymous reviewer, whose valuable input has added much to this paper.

Funding

The authors gratefully acknowledge the support of the DARPA Defense Sciences office; EAL also thanks the US Department of Defense for an NDSEG fellowship. The authors would also like to thank the anonymous reviewer, whose valuable input has added much to this paper.

Funders	Funder number
U.S. Department of Defense
Defense Advanced Research Projects Agency

Keywords

Grain growth
Simulation
von Neumann-Mullins theory

Access to Document

10.1016/j.actamat.2009.09.008

Cite this

@article{6b9e5cf270a9431aadd65bc9b945f752,

title = "A more accurate two-dimensional grain growth algorithm",

abstract = "We describe a method for evolving two-dimensional polycrystalline microstructures via mean curvature flow that satisfies the von Neumann-Mullins relation with an absolute error O (Δ t2). This is a significant improvement over a different method currently used that has an absolute error O (Δ t). We describe the implementation of this method and show that while both approaches lead to indistinguishable evolution when the spatial discretization is very fine, the differences can be substantial when the discretization is left unrefined. We demonstrate that this new front-tracking approach can be pushed to the limit in which the only mesh nodes are those coincident with triple junctions. This reduces the method to a vertex model that is consistent with the exact kinetic law for grain growth. We briefly discuss an extension of the method to higher spatial dimensions.",

keywords = "Grain growth, Simulation, von Neumann-Mullins theory",

author = "Lazar, {Emanuel A.} and MacPherson, {Robert D.} and Srolovitz, {David J.}",

note = "Funding Information: The authors gratefully acknowledge the support of the DARPA Defense Sciences office; EAL also thanks the US Department of Defense for an NDSEG fellowship. The authors would also like to thank the anonymous reviewer, whose valuable input has added much to this paper.",

year = "2010",

month = jan,

doi = "10.1016/j.actamat.2009.09.008",

language = "אנגלית",

volume = "58",

pages = "364--372",

journal = "Acta Materialia",

issn = "1359-6454",

publisher = "Acta Materialia Inc",

number = "2",

}

TY - JOUR

T1 - A more accurate two-dimensional grain growth algorithm

AU - Lazar, Emanuel A.

AU - MacPherson, Robert D.

AU - Srolovitz, David J.

N1 - Funding Information: The authors gratefully acknowledge the support of the DARPA Defense Sciences office; EAL also thanks the US Department of Defense for an NDSEG fellowship. The authors would also like to thank the anonymous reviewer, whose valuable input has added much to this paper.

PY - 2010/1

Y1 - 2010/1

N2 - We describe a method for evolving two-dimensional polycrystalline microstructures via mean curvature flow that satisfies the von Neumann-Mullins relation with an absolute error O (Δ t2). This is a significant improvement over a different method currently used that has an absolute error O (Δ t). We describe the implementation of this method and show that while both approaches lead to indistinguishable evolution when the spatial discretization is very fine, the differences can be substantial when the discretization is left unrefined. We demonstrate that this new front-tracking approach can be pushed to the limit in which the only mesh nodes are those coincident with triple junctions. This reduces the method to a vertex model that is consistent with the exact kinetic law for grain growth. We briefly discuss an extension of the method to higher spatial dimensions.

AB - We describe a method for evolving two-dimensional polycrystalline microstructures via mean curvature flow that satisfies the von Neumann-Mullins relation with an absolute error O (Δ t2). This is a significant improvement over a different method currently used that has an absolute error O (Δ t). We describe the implementation of this method and show that while both approaches lead to indistinguishable evolution when the spatial discretization is very fine, the differences can be substantial when the discretization is left unrefined. We demonstrate that this new front-tracking approach can be pushed to the limit in which the only mesh nodes are those coincident with triple junctions. This reduces the method to a vertex model that is consistent with the exact kinetic law for grain growth. We briefly discuss an extension of the method to higher spatial dimensions.

KW - Grain growth

KW - Simulation

KW - von Neumann-Mullins theory

UR - http://www.scopus.com/inward/record.url?scp=70449508064&partnerID=8YFLogxK

U2 - 10.1016/j.actamat.2009.09.008

DO - 10.1016/j.actamat.2009.09.008

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:70449508064

SN - 1359-6454

VL - 58

SP - 364

EP - 372

JO - Acta Materialia

JF - Acta Materialia

IS - 2

ER -

A more accurate two-dimensional grain growth algorithm

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this