Lattice boltzmann method and kinetic theory

S. Ansumali; S. S. Chikatamarla; C. E. Frouzakis; I. V. Karlin; I. G. Kevrekidis

doi:10.1007/3-540-35888-9_18

Lattice boltzmann method and kinetic theory

S. Ansumali, S. S. Chikatamarla, C. E. Frouzakis, I. V. Karlin, I. G. Kevrekidis

Chemical & Biological Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

2 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena
Publisher	Springer Berlin Heidelberg
Pages	403-422
Number of pages	20
ISBN (Print)	3540358854, 9783540358855
DOIs	https://doi.org/10.1007/3-540-35888-9_18
State	Published - Dec 1 2006

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1007/3-540-35888-9_18

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AU - Ansumali, S.

AU - Chikatamarla, S. S.

AU - Frouzakis, C. E.

AU - Karlin, I. V.

AU - Kevrekidis, I. G.

PY - 2006/12/1

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AB - 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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Lattice boltzmann method and kinetic theory

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