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Lattice-Boltzmann coupled models for advection–diffusion flow on a wide range of Péclet numbers

Dapelo, Davide; Simonis, Stephan ORCID iD icon 1; Krause, Mathias J. 1; Bridgeman, John
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

Traditional Lattice-Boltzmann modelling of advection–diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier–Stokes solver is coupled to a Lattice-Boltzmann advection–diffusion model. In a novel model, the Lattice-Boltzmann Navier–Stokes solver is coupled to an explicit finite-difference algorithm for advection–diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme.

The models are validated using two non-trivial benchmarks, which includes discontinuous initial conditions and the case Pe$_{g}$->$\infty$ for the first time, where Pe$_{g}$ is the grid Péclet number. The evaluation of Pe$_{g}$ alongside Pe is discussed. Accuracy, stability and the order of convergence are assessed for a wide range of Péclet numbers. Recommendations are then given as to which model to select depending on the value Pe$_{g}$ - in particular, it is shown that the coupled finite-difference/Lattice-Boltzmann provide stable solutions in the case Pe->$\infty$, Pe$_{g}$->$\infty$


Verlagsausgabe §
DOI: 10.5445/IR/1000131669
Veröffentlicht am 23.04.2021
Originalveröffentlichung
DOI: 10.1016/j.jocs.2021.101363
Scopus
Zitationen: 12
Web of Science
Zitationen: 13
Dimensions
Zitationen: 17
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 1877-7503, 1877-7511
KITopen-ID: 1000131669
Erschienen in Journal of Computational Science
Verlag Elsevier
Band 51
Seiten Art.-Nr.: 101363
Schlagwörter Lattice-Boltzmann; OpenLB; Advection–diffusion; Finite-difference
Nachgewiesen in Web of Science
Dimensions
Scopus
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