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.
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Chalupecký, V., Eck, C. & Emmerich, H. Computation of nonlinear multiscale coupling effects in liquid phase epitaxy. Eur. Phys. J. Spec. Top. 149, 1–17 (2007). https://doi.org/10.1140/epjst/e2007-00240-6
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DOI: https://doi.org/10.1140/epjst/e2007-00240-6