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Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations: Pattern Formation Under Uniform Differential Advection

Published online by Cambridge University Press:  03 June 2015

S. G. Ayodele ,
D. Raabe  and
F. Varnik
S. G. Ayodele*
Affiliation:
Max-Planck Institut für, Eisenforschung, Max-Planck Straße 1, 40237, Düsseldorf, Germany
D. Raabe*
Affiliation:
Max-Planck Institut für, Eisenforschung, Max-Planck Straße 1, 40237, Düsseldorf, Germany
F. Varnik*
Affiliation:
Max-Planck Institut für, Eisenforschung, Max-Planck Straße 1, 40237, Düsseldorf, Germany Interdisciplinary Center for Advanced Materials Simulation, Ruhr University Bochum, Stiepeler Straße 129, 44780 Bochum, Germany
*
Corresponding author.Email:s.ayodele@mpie.de
Email:d.raabe@mpie.de
Email:fathollah.varnik@rub.de
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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 from the interaction of advective transport with a cubic autocatalytic reaction-diffusion process under an imposed uniform flow. While advecting all the present species leads to trivial translation of the Turing patterns, differential advection leads to 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.

Keywords

76R0576R5092C1580A32Advective transportdifferential advectionTuring patternslinear stabilitylattice Boltzmann
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 3 , March 2013 , pp. 741 - 756
Copyright
Copyright © Global Science Press Limited 2013

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