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Lattice Boltzmann Method and Kinetic Theory

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Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

Summary

One of the classical questions of non-equilibrium thermodynamics is the validity of various closure approximations in nontrivial flows. We study this question for a lid-driven cavity flow using a minimal molecular model derived from the Boltzmann equation. In this nontrivial flow, we quantify the model as a superset of the Grad moment approximation and visualize the quality of the Chapman-Enskog and Grad closure approximations. It is found that the Grad closure approximation is strikingly more robust than the Chapman-Enskog approximation at all Knudsen numbers studied. Grad’s approximation is used to formulate a novel outflow boundary condition for lattice Boltzmann simulations.

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Author information

Authors and Affiliations

  1. School of Chemical and Biomedical Engineering, Nanyang Technological University, 639798, Singapore

    S. Ansumali

  2. Aerothermochemistry and Combustion Systems Laboratory, ETH Zurich, 8092, Zürich, Switzerland

    S. S. Chikatamarla, C. E. Frouzakis & I. V. Karlin

  3. Department of Chemical Engineering, Princeton University, NJ, 08544-5263, USA

    I. G. Kevrekidis

Authors
  1. S. Ansumali
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  2. S. S. Chikatamarla
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  3. C. E. Frouzakis
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  4. I. V. Karlin
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  5. I. G. Kevrekidis
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Alexander N. Gorban

  2. Institute of Computational Modeling, Russian Academy of Sciences, Russia

    Alexander N. Gorban

  3. Department of Chemical Engineering, Princeton University, Engineering Quadrangle A-217, Princeton, NJ, 08544-5263, USA

    Ioannis G. Kevrekidis

  4. School of Chemical Engineering and Analytical Science, University of Manchester, PO Box 88, Sackville St., Manchester, M60 1QD, UK

    Constantinos Theodoropoulos

  5. Department of Chemical Engineering, Worcester Polytechnic Institute, Institute Road 100, Worcester, MA, 01609-2280, USA

    Nikolaos K. Kazantzis

  6. Institut für Polymere, ETH Zürich, Wolfgang Pauli-Straße 10, CH-8093, Zürich, Switzerland

    Hans Christian Öttinger

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© 2006 Springer-Verlag Berlin Heidelberg

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Ansumali, S., Chikatamarla, S.S., Frouzakis, C.E., Karlin, I.V., Kevrekidis, I.G. (2006). Lattice Boltzmann Method and Kinetic Theory. In: Gorban, A.N., Kevrekidis, I.G., Theodoropoulos, C., Kazantzis, N.K., Öttinger, H.C. (eds) Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35888-9_18

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