Strategies for the coupling of global and local crystal growth models

Jeffrey J. Derby; Lisa Lun; Andrew Yeckel

doi:10.1016/j.jcrysgro.2006.11.343

Strategies for the coupling of global and local crystal growth models

Jeffrey J. Derby, Lisa Lun, Andrew Yeckel

Chemical Engineering and Materials Science

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

19 Scopus citations

Abstract

The modular coupling of existing numerical codes to model crystal growth processes will provide for maximum effectiveness, capability, and flexibility. However, significant challenges are posed to make these coupled models mathematically self-consistent and algorithmically robust. This paper presents sample results from a coupling of the CrysVUn code, used here to compute furnace-scale heat transfer, and Cats2D, used to calculate melt fluid dynamics and phase-change phenomena, to form a global model for a Bridgman crystal growth system. However, the strategy used to implement the CrysVUn-Cats2D coupling is unreliable and inefficient. The implementation of under-relaxation within a block Gauss-Seidel iteration is shown to be ineffective for improving the coupling performance in a model one-dimensional problem representative of a melt crystal growth model. Ideas to overcome current convergence limitations using approximations to a full Newton iteration method are discussed.

Original language	English (US)
Pages (from-to)	114-123
Number of pages	10
Journal	Journal of Crystal Growth
Volume	303
Issue number	1 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.jcrysgro.2006.11.343
State	Published - May 1 2007

Bibliographical note

Funding Information:
This material is based upon work supported in part by the National Science Foundation, under Grant no. 0201486, and the Department of Energy, National Nuclear Security Administration, under Award Numbers DE-FC07-06ID14726 and DE-FG52-06NA27498, the content of which does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred. Computational resources were provided by the Minnesota Supercomputing Institute. The authors wish to thank our collaborators, Jochen Friedrich, Georg Müller, Thomas Jung, and Jakob Fainberg of the Crystal Growth Laboratory of the Fraunhofer Institute IISB for motivation and significant input to aspects of this research.

Keywords

A1. Computer simulation
A1. Directional solidification
A1. Heat transfer
A2. Bridgman technique
A2. Growth from melt

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title = "Strategies for the coupling of global and local crystal growth models",

abstract = "The modular coupling of existing numerical codes to model crystal growth processes will provide for maximum effectiveness, capability, and flexibility. However, significant challenges are posed to make these coupled models mathematically self-consistent and algorithmically robust. This paper presents sample results from a coupling of the CrysVUn code, used here to compute furnace-scale heat transfer, and Cats2D, used to calculate melt fluid dynamics and phase-change phenomena, to form a global model for a Bridgman crystal growth system. However, the strategy used to implement the CrysVUn-Cats2D coupling is unreliable and inefficient. The implementation of under-relaxation within a block Gauss-Seidel iteration is shown to be ineffective for improving the coupling performance in a model one-dimensional problem representative of a melt crystal growth model. Ideas to overcome current convergence limitations using approximations to a full Newton iteration method are discussed.",

keywords = "A1. Computer simulation, A1. Directional solidification, A1. Heat transfer, A2. Bridgman technique, A2. Growth from melt",

author = "Derby, {Jeffrey J.} and Lisa Lun and Andrew Yeckel",

note = "Funding Information: This material is based upon work supported in part by the National Science Foundation, under Grant no. 0201486, and the Department of Energy, National Nuclear Security Administration, under Award Numbers DE-FC07-06ID14726 and DE-FG52-06NA27498, the content of which does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred. Computational resources were provided by the Minnesota Supercomputing Institute. The authors wish to thank our collaborators, Jochen Friedrich, Georg M{\"u}ller, Thomas Jung, and Jakob Fainberg of the Crystal Growth Laboratory of the Fraunhofer Institute IISB for motivation and significant input to aspects of this research. ",

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AU - Yeckel, Andrew

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PY - 2007/5/1

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N2 - The modular coupling of existing numerical codes to model crystal growth processes will provide for maximum effectiveness, capability, and flexibility. However, significant challenges are posed to make these coupled models mathematically self-consistent and algorithmically robust. This paper presents sample results from a coupling of the CrysVUn code, used here to compute furnace-scale heat transfer, and Cats2D, used to calculate melt fluid dynamics and phase-change phenomena, to form a global model for a Bridgman crystal growth system. However, the strategy used to implement the CrysVUn-Cats2D coupling is unreliable and inefficient. The implementation of under-relaxation within a block Gauss-Seidel iteration is shown to be ineffective for improving the coupling performance in a model one-dimensional problem representative of a melt crystal growth model. Ideas to overcome current convergence limitations using approximations to a full Newton iteration method are discussed.

AB - The modular coupling of existing numerical codes to model crystal growth processes will provide for maximum effectiveness, capability, and flexibility. However, significant challenges are posed to make these coupled models mathematically self-consistent and algorithmically robust. This paper presents sample results from a coupling of the CrysVUn code, used here to compute furnace-scale heat transfer, and Cats2D, used to calculate melt fluid dynamics and phase-change phenomena, to form a global model for a Bridgman crystal growth system. However, the strategy used to implement the CrysVUn-Cats2D coupling is unreliable and inefficient. The implementation of under-relaxation within a block Gauss-Seidel iteration is shown to be ineffective for improving the coupling performance in a model one-dimensional problem representative of a melt crystal growth model. Ideas to overcome current convergence limitations using approximations to a full Newton iteration method are discussed.

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Strategies for the coupling of global and local crystal growth models

Abstract

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