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The European Physical Journal Special Topics

, Volume 149, Issue 1, pp 1–17 | Cite as

Computation of nonlinear multiscale coupling effects in liquid phase epitaxy

  • V. Chalupecký
  • Ch. Eck
  • H. Emmerich
Article

Abstract.

A new two-scale model for liquid phase epitaxy is presented which enables the numerical simulation of processes with microstructures having an arbitrarily small scale. It is based on a BCF-model for epitaxial growth, a Navier–Stokes system and a convection-diffusion equation. The application of a homo- genization approach leads to a separation of scales; the resulting two-scale model consists of macroscopic partial differential equations for fluid flow and solute diffusion in the fluid volume, coupled to microscopic BCF-models. The two-scale model can be discretized using grids that are independent of the scale of the microstructure. Numerical experiments based on a phase field version of the BCF model are presented; the results illustrate the physical relevance of the model.

Keywords

European Physical Journal Special Topic Epitaxial Layer Liquid Phase Epitaxy Dislocation Cell Lead Order Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • V. Chalupecký
    • 1
  • Ch. Eck
    • 2
  • H. Emmerich
    • 3
  1. 1.Department of MathematicsFaculty of Nuclear Science and Physical Engineering, Czech Technical University in PraguePragueCzech Republic
  2. 2.Institute for Applied Mathematics, Friedrich-Alexander UniversityErlangenGermany
  3. 3.Computational Materials Engineering, Center for Computational Engineering Science, Institute of Minerals Engineering, RWTH Aachen UniversityAachenGermany

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