A Level Set Approach for the Numerical Simulation of Dendritic Growth

Frédéric Gibou; Ronald Fedkiw; Russel Caflisch; Stanley Osher

doi:10.1023/A:1025399807998

A Level Set Approach for the Numerical Simulation of Dendritic Growth

Frédéric Gibou, Ronald Fedkiw, Russel Caflisch, Stanley Osher

Mathematics

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

Abstract

In this paper, we present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of the Poisson equation, see [12]. Numerical results indicate that this method can be used successfully on complex intsrfacial shapes and can simulate many of the physical features of dendritic solidification. We apply this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results are presented in both two and three spatial dimensions.

Original language	English (US)
Pages (from-to)	183-199
Number of pages	17
Journal	Journal of Scientific Computing
Volume	19
Issue number	1-3
DOIs	https://doi.org/10.1023/A:1025399807998
State	Published - Dec 2003

Keywords

Dendritic growth
Ghost fluid method
Interfaces
Level set method
Poisson equation

ASJC Scopus subject areas

Software
General Engineering
Computational Mathematics
Theoretical Computer Science
Applied Mathematics
Numerical Analysis
Computational Theory and Mathematics

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10.1023/A:1025399807998

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@article{dcc5ae9e686a4b968945363452facdaa,

title = "A Level Set Approach for the Numerical Simulation of Dendritic Growth",

abstract = "In this paper, we present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of the Poisson equation, see [12]. Numerical results indicate that this method can be used successfully on complex intsrfacial shapes and can simulate many of the physical features of dendritic solidification. We apply this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results are presented in both two and three spatial dimensions.",

keywords = "Dendritic growth, Ghost fluid method, Interfaces, Level set method, Poisson equation",

author = "Fr{\'e}d{\'e}ric Gibou and Ronald Fedkiw and Russel Caflisch and Stanley Osher",

note = "Funding Information: F.G. was supported in part by an NSF postdoctoral fellowship # DMS-0102029, a Focused Research Group Grant # DMS0074152 from the NSF and by ONR N00014-01-1-0620. R.F. was supported in part by an ONR YIP and PECASE award N00014-01-1-0620 and NSF-0106694. R.C. was supported in part by a Focused Research Group Grant # DMS0074152 from the NSF. S.O. was supported in part by ONR N00014-97-0027 and NSF DMS-0074735.",

year = "2003",

month = dec,

doi = "10.1023/A:1025399807998",

language = "English (US)",

volume = "19",

pages = "183--199",

journal = "Journal of Scientific Computing",

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AU - Gibou, Frédéric

AU - Fedkiw, Ronald

AU - Caflisch, Russel

AU - Osher, Stanley

N1 - Funding Information: F.G. was supported in part by an NSF postdoctoral fellowship # DMS-0102029, a Focused Research Group Grant # DMS0074152 from the NSF and by ONR N00014-01-1-0620. R.F. was supported in part by an ONR YIP and PECASE award N00014-01-1-0620 and NSF-0106694. R.C. was supported in part by a Focused Research Group Grant # DMS0074152 from the NSF. S.O. was supported in part by ONR N00014-97-0027 and NSF DMS-0074735.

PY - 2003/12

Y1 - 2003/12

N2 - In this paper, we present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of the Poisson equation, see [12]. Numerical results indicate that this method can be used successfully on complex intsrfacial shapes and can simulate many of the physical features of dendritic solidification. We apply this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results are presented in both two and three spatial dimensions.

AB - In this paper, we present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of the Poisson equation, see [12]. Numerical results indicate that this method can be used successfully on complex intsrfacial shapes and can simulate many of the physical features of dendritic solidification. We apply this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results are presented in both two and three spatial dimensions.

KW - Dendritic growth

KW - Ghost fluid method

KW - Interfaces

KW - Level set method

KW - Poisson equation

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JO - Journal of Scientific Computing

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A Level Set Approach for the Numerical Simulation of Dendritic Growth

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Keywords

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