https://doi.org/10.1140/epjst/e2007-00240-6
Computation of nonlinear multiscale coupling effects in liquid phase epitaxy
1
Department of Mathematics, Faculty of Nuclear Science and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
2
Institute for Applied Mathematics, Friedrich-Alexander University, Erlangen-Nuremberg, Martensstrasse 3, 91058 Erlangen, Germany
3
Computational Materials Engineering, Center for Computational Engineering Science, Institute of Minerals Engineering, RWTH Aachen University, Mauerstrasse 5, 52064 Aachen, Germany
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.
© EDP Sciences, Springer-Verlag, 2007
