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Center for Nonlinear Studies |
We introduce the multiscale methods for interface tracking and apply the technique to the simulation of combustion fronts and epitaxial growth. Our approach overcomes the numerical difficulties caused by different time/length scales between the transport and reactive parts in the combustion model. The approach relies on an efficient coupling between macroscale and microscale models. When the macroscale model is not fully known explicitly or not valid in localized regions, the method provides a procedure for supplementing the missing data from a microscale model. A front tracking method defines the interface on the macroscale. Numerical results for different models, including reactive Euler equations in 1D and 2D show the efficiency of our approach. The planed work on coupling level set method and kinetic Monte Carlo simulation for epitaxial growth will also be presented.