Title
Accuracy of hybrid lattice Boltzmann/finite difference schemes for reaction-diffusion systems Accuracy of hybrid lattice Boltzmann/finite difference schemes for reaction-diffusion systems
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Computer. Automation
Source (journal)
Multiscale modeling and simulation
Volume/pages
6(2007) :3 , p. 838-857
ISSN
1540-3459
ISI
000252254800006
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In this article we construct a hybrid model by spatially coupling a lattice Boltzmann model (LBM) to a finite difference discretization of the partial differential equation (PDE) for reaction-diffusion systems. Because the LBM has more variables (the particle distribution functions) than the PDE (only the particle density), we have a one-to-many mapping problem from the PDE to the LBM domain at the interface. We perform this mapping using either results from the ChapmanEnskog expansion or a pointwise iterative scheme that approximates these analytical relations numerically. Most importantly, we show that the global spatial discretization error of the hybrid model is one order less accurate than the local error made at the interface. We derive closed expressions for the spatial discretization error at steady state and verify them numerically for several examples on the one-dimensional domain.
E-info
http://dx.doi.org/10.1137/060675113
Full text (open access)
https://repository.uantwerpen.be/docman/irua/dad54b/4502.pdf
E-info
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