We study a numerical closure approach for systems of chemically reacting systems on lattices with low-dimensional support, for which a mean-field approximation is insufficiently accurate because of lateral interaction on the lattice. We introduce a hierarchy of macroscopic state variables, taking particle clusters into account, whose time evolution is obtained via microscopic (kinetic Monte Carlo) simulation. The macroscopic state variables are chosen such that they can be straightforwardly conserved during reconstruction of a microscopic configuration (the so-called lifting step). We present and compare the effects of different alternatives to initialize the remaining degrees of freedom. We illustrate the strong interplay between the number of macroscopic state variables and the specifics of the lifting and that, for a given lifting operator, accuracy of the macroscopic dynamics does not necessarily improve monotonically when adding macroscopic state variables.
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28 November 2012
Research Article|
November 27 2012
Towards an efficient multiscale modeling of low-dimensional reactive systems: Study of numerical closure procedures
Giacomo Mazzi;
Giacomo Mazzi
1
Scientific Computing
, Department of Computer Science, KU Leuven, Leuven, Belgium
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Yannick De Decker;
Yannick De Decker
2Interdisciplinary Center for Nonlinear Phenomena and Complex Systems (CENOLI),
Université Libre de Bruxelles
, Bruxelles, Belgium
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Giovanni Samaey
Giovanni Samaey
a)
1
Scientific Computing
, Department of Computer Science, KU Leuven, Leuven, Belgium
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a)
Author to whom correspondence should be addressed. Electronic mail: [email protected].
J. Chem. Phys. 137, 204115 (2012)
Article history
Received:
April 19 2012
Accepted:
October 12 2012
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Citation
Giacomo Mazzi, Yannick De Decker, Giovanni Samaey; Towards an efficient multiscale modeling of low-dimensional reactive systems: Study of numerical closure procedures. J. Chem. Phys. 28 November 2012; 137 (20): 204115. https://doi.org/10.1063/1.4764109
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