Computing the effective diffusivity using a spectral method

Jingzhi Zhu; Long Qing Chen; Jie Shen; Veena Tikare

doi:10.1016/S0921-5093(01)00961-3

Computing the effective diffusivity using a spectral method

Jingzhi Zhu, Long Qing Chen, Jie Shen, Veena Tikare

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

11 Scopus citations

Abstract

We developed a numerical method for computing the effective properties of a microstructure. The method is particularly efficient and accurate for microstructures with a diffuse-interface description similar to those generated from phase-field simulations. In particular, we considered the diffusive transport property of a microstructure by solving the steady-state diffusion equation using a Fourier-Chebyshev spectral method. Computed effective diffusivities agree very well with existing analytical solutions and computer simulations for a number of simple model systems. Combining with the phase-field model for simulating microstructure evolution, the proposed method can be applied for modeling the temporal evolution of effective properties. This is illustrated by considering grain growth and the corresponding effective transport property evolution as function of time.

Original language	English (US)
Pages (from-to)	135-141
Number of pages	7
Journal	Materials Science and Engineering: A
Volume	311
Issue number	1-2
DOIs	https://doi.org/10.1016/S0921-5093(01)00961-3
State	Published - Jul 31 2001

All Science Journal Classification (ASJC) codes

General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

Access to Document

10.1016/S0921-5093(01)00961-3

Cite this

@article{a87a829b9a324143adc3eb2afb136c13,

title = "Computing the effective diffusivity using a spectral method",

abstract = "We developed a numerical method for computing the effective properties of a microstructure. The method is particularly efficient and accurate for microstructures with a diffuse-interface description similar to those generated from phase-field simulations. In particular, we considered the diffusive transport property of a microstructure by solving the steady-state diffusion equation using a Fourier-Chebyshev spectral method. Computed effective diffusivities agree very well with existing analytical solutions and computer simulations for a number of simple model systems. Combining with the phase-field model for simulating microstructure evolution, the proposed method can be applied for modeling the temporal evolution of effective properties. This is illustrated by considering grain growth and the corresponding effective transport property evolution as function of time.",

author = "Jingzhi Zhu and Chen, {Long Qing} and Jie Shen and Veena Tikare",

note = "Funding Information: The authors are grateful for the financial support from the Sandia National Laboratory and the National Science Foundation under Grant No. DMR 96-33719 and DMS 9721413. Copyright: Copyright 2007 Elsevier B.V., All rights reserved.",

year = "2001",

month = jul,

day = "31",

doi = "10.1016/S0921-5093(01)00961-3",

language = "English (US)",

volume = "311",

pages = "135--141",

journal = "Materials Science and Engineering: A",

issn = "0921-5093",

publisher = "Elsevier Ltd",

number = "1-2",

}

TY - JOUR

T1 - Computing the effective diffusivity using a spectral method

AU - Zhu, Jingzhi

AU - Chen, Long Qing

AU - Shen, Jie

AU - Tikare, Veena

N1 - Funding Information: The authors are grateful for the financial support from the Sandia National Laboratory and the National Science Foundation under Grant No. DMR 96-33719 and DMS 9721413. Copyright: Copyright 2007 Elsevier B.V., All rights reserved.

PY - 2001/7/31

Y1 - 2001/7/31

N2 - We developed a numerical method for computing the effective properties of a microstructure. The method is particularly efficient and accurate for microstructures with a diffuse-interface description similar to those generated from phase-field simulations. In particular, we considered the diffusive transport property of a microstructure by solving the steady-state diffusion equation using a Fourier-Chebyshev spectral method. Computed effective diffusivities agree very well with existing analytical solutions and computer simulations for a number of simple model systems. Combining with the phase-field model for simulating microstructure evolution, the proposed method can be applied for modeling the temporal evolution of effective properties. This is illustrated by considering grain growth and the corresponding effective transport property evolution as function of time.

AB - We developed a numerical method for computing the effective properties of a microstructure. The method is particularly efficient and accurate for microstructures with a diffuse-interface description similar to those generated from phase-field simulations. In particular, we considered the diffusive transport property of a microstructure by solving the steady-state diffusion equation using a Fourier-Chebyshev spectral method. Computed effective diffusivities agree very well with existing analytical solutions and computer simulations for a number of simple model systems. Combining with the phase-field model for simulating microstructure evolution, the proposed method can be applied for modeling the temporal evolution of effective properties. This is illustrated by considering grain growth and the corresponding effective transport property evolution as function of time.

UR - http://www.scopus.com/inward/record.url?scp=0035979463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035979463&partnerID=8YFLogxK

U2 - 10.1016/S0921-5093(01)00961-3

DO - 10.1016/S0921-5093(01)00961-3

M3 - Article

AN - SCOPUS:0035979463

SN - 0921-5093

VL - 311

SP - 135

EP - 141

JO - Materials Science and Engineering: A

JF - Materials Science and Engineering: A

IS - 1-2

ER -

Computing the effective diffusivity using a spectral method

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this