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arXiv · 1108.6222

The Effect of Nonlinearity in Hybrid KMC-Continuum models

Ariel Balter·Guang Lin·Alexandre M. Tartakovsky
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Abstract

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a KMC model for a surface to a finite difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and also show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition/dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition/dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that, in this case, the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

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Ariel Balter, Guang Lin, Alexandre M. Tartakovsky. 2011-08-26. The Effect of Nonlinearity in Hybrid KMC-Continuum models. https://doi.org/10.1103/physreve.85.016707

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