Computation of nonlinear multiscale coupling effects in liquid phase epitaxy
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