Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations: Pattern Formation Under Uniform Differential Advection
Year: 2013
Communications in Computational Physics, Vol. 13 (2013), Iss. 3 : pp. 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 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.441011.270112s
Communications in Computational Physics, Vol. 13 (2013), Iss. 3 : pp. 741–756
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
-
A discrete reactive collision scheme for the lattice Boltzmann method
Pribec, Ivan | Hubman, Anže | Urbic, Tomaz | Plazl, IgorJournal of Molecular Liquids, Vol. 332 (2021), Iss. P.115871
https://doi.org/10.1016/j.molliq.2021.115871 [Citations: 3] -
Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flow with large viscosity ratio and high Péclet number
Meng, Xuhui | Guo, ZhaoliPhysical Review E, Vol. 92 (2015), Iss. 4
https://doi.org/10.1103/PhysRevE.92.043305 [Citations: 50] -
Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations
Yang, Xuguang | Shi, Baochang | Chai, ZhenhuaPhysical Review E, Vol. 90 (2014), Iss. 1
https://doi.org/10.1103/PhysRevE.90.013309 [Citations: 32] -
Shear-flow-controlled mode selection in a nonlinear autocatalytic medium
Ayodele, S. G. | Raabe, D. | Varnik, F.Physical Review E, Vol. 91 (2015), Iss. 2
https://doi.org/10.1103/PhysRevE.91.022913 [Citations: 1] -
A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes
Bartlett, Stuart
Computation, Vol. 5 (2017), Iss. 3 P.37
https://doi.org/10.3390/computation5030037 [Citations: 3] -
Lattice Boltzmann Modeling for Chemical Engineering
LBM for separation processes
Majumder, Aniruddha
2020
https://doi.org/10.1016/bs.ache.2020.04.002 [Citations: 0] -
Stability limits of the single relaxation-time advection–diffusion lattice Boltzmann scheme
Hosseini, Seyed Ali | Darabiha, Nasser | Thévenin, Dominique | Eshghinejadfard, AmirInternational Journal of Modern Physics C, Vol. 28 (2017), Iss. 12 P.1750141
https://doi.org/10.1142/S0129183117501418 [Citations: 26]