Volume 13, Issue 3
Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations: Pattern Formation Under Uniform Differential Advection

S. G. Ayodele, D. Raabe & F. Varnik

Commun. Comput. Phys., 13 (2013), pp. 741-756.

Published online: 2013-03

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  • Abstract

A lattice Boltzmann model for the study of advection-diffusion-reaction (ADR) problems is proposed. Via multiscale expansion analysis, we derive from the LB model the resulting macroscopic equations. It is shown that a linear equilibrium distribution is sufficient to produce ADR equations within error terms of the order of the Mach number squared. Furthermore, we study spatially varying structures arising fromthe interactionof advectivetransportwithacubicautocatalyticreaction-diffusion process under an imposed uniform flow. While advecting all the present species leads to trivial translationof the Turing patterns, differentialadvectionleadsto flow induced instability characterized with traveling stripes with a velocity dependent wave vector parallel to the flow direction. Predictions from a linear stability analysis of the model equations are found to be in line with these observations. 

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@Article{CiCP-13-741, author = {S. G. Ayodele, D. Raabe and F. Varnik}, title = {Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations: Pattern Formation Under Uniform Differential Advection}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {3}, pages = {741--756}, abstract = {

A lattice Boltzmann model for the study of advection-diffusion-reaction (ADR) problems is proposed. Via multiscale expansion analysis, we derive from the LB model the resulting macroscopic equations. It is shown that a linear equilibrium distribution is sufficient to produce ADR equations within error terms of the order of the Mach number squared. Furthermore, we study spatially varying structures arising fromthe interactionof advectivetransportwithacubicautocatalyticreaction-diffusion process under an imposed uniform flow. While advecting all the present species leads to trivial translationof the Turing patterns, differentialadvectionleadsto flow induced instability characterized with traveling stripes with a velocity dependent wave vector parallel to the flow direction. Predictions from a linear stability analysis of the model equations are found to be in line with these observations. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.441011.270112s}, url = {http://global-sci.org/intro/article_detail/cicp/7247.html} }
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