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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v3.i2.80
pages 239-256

Mixed KMC-Continuum Models for the Evolution of Rough Surfaces

Simon P.A. Gill
Department of Engineering, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom
Paul E. Spencer
Department of Engineering, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom
Alan C. E. Cocks
Department of Engineering, University of Leicester, University Road Leicester, LE1 7RH, United Kingdom

ABSTRACT

An atomistic solid-on-solid (SOS) kinetic Monte Carlo (KMC) model for surface diffusion is found to exhibit curvature-driven decay. An equivalent continuum Mullins-Herring equation is derived and the two systems are shown to be compatible. A mixed KMC-continuum model is proposed that allows discrete atomistic simulations to be embedded within a smooth continuum. A blending region is introduced between the two model descriptions, which allow mass to be transferred between them in a consistent manner. The implementation of this multiscale modeling approach is illustrated with simulations of the decay of a sinusoid and a Gaussian peak.


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