Commun. Comput. Phys.,
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Volume 3.


A Numerical Investigation for a Model of the Solid-Gas Phase in a Crystal Growth Apparatus

Jurgen Geiser 1*

1 Humboldt-Universitat zu Berlin, Department of Mathematics Unter den Linden 6, D-10099 Berlin, Germany.

Received 22 December 2006; Accepted (in revised version) 6 September 2007
Available online 11 December 2007

Abstract

We present discretization and solver methods for a model of the solid-gas phase in a crystal growth apparatus. The model equations are coupled Eulerian and heat-transfer equations with flux boundary conditions. For a more detailed discussion we consider simpler equations and present time- and space-decomposition methods as solver methods to decouple the multi-physics processes. We present the error analysis for the discretization and solver methods. Numerical experiments are performed for the Eulerian and heat-transfer equation using decomposition methods. We present a real-life application of a crystal growth apparatus, based on underlying stationary heat conduction. Finally we discuss further error analysis and application to a more complex model of crystal growth.

AMS subject classifications: 74S10, 80A20, 47F05, 65M60, 80M25, 49M27
PACS: 02.60.Cb, 02.60.-x, 44.05.+e, 47.10.ab, 47.11.Df, 47.11.St, 47.27.te
Key words: Decomposition methods, finite-volume discretization, error analysis, heat equation, crystal growth.

*Corresponding author.
Email: geiser@mathematik.hu-berlin.de (J. Geiser)
 

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