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Entropic lattice Boltzmann method for microflows

Entropic lattice Boltzmann method for microflows
Entropic lattice Boltzmann method for microflows
A new method for the computation of flows at the micrometer scale is presented. It is based oil the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice Bhatnagar-Gross-Krook (ELBGK) is studied ill detail in order to quantify its relevance for microflow simulations. ELBGK is equipped with boundary conditions which are derived from molecular models (diffusive wall). A map of three-dimensional kinetic equations onto two-dimensional models is established which enables two-dimensional Simulations of quasi-two-dimensional flows. The ELBGK model is studied extensively in the simulation of the two-dimensional Poiseuille channel flow. Results are compared to known analytical and numerical studies of this flow in the setting of the Bhatnagar-Gross-Krook model. The ELBGK is ill quantitative agreement with analytical results in the domain of weak rarefaction (characterized by Knudsen number Kn, the ratio of mean free path to the hydrodynamic scale), up to Kn similar to 0.01, which is the domain of many practical microflows. Moreover, the results qualitatively agree throughout the entire Knudsen number range, demonstrating Knudsen's minimum for the mass flow rate at moderate values of Kn, as well as the logarithmic scaling at large Kn. The present results indicate that ELBM can complement or even replace computationally expensive microscopic simulation techniques such as kinetic Monte Carlo and/or molecular dynamics for low Mach and low Knudsen number hydrodynamics pertinent to microflows.
0378-4371
289-305
Ansumali, S.
419cb861-d1f8-4532-a1ab-2b56135391b5
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Frouzakis, C.E.
69f46c40-d7f7-41f3-a166-c0311158b821
Boulouchos, K.B.
48d28ebe-3928-4afe-9490-c107305b072c
Ansumali, S.
419cb861-d1f8-4532-a1ab-2b56135391b5
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Frouzakis, C.E.
69f46c40-d7f7-41f3-a166-c0311158b821
Boulouchos, K.B.
48d28ebe-3928-4afe-9490-c107305b072c

Ansumali, S., Karlin, I.V., Frouzakis, C.E. and Boulouchos, K.B. (2006) Entropic lattice Boltzmann method for microflows. Physica A: Statistical Mechanics and its Applications, 359, 289-305. (doi:10.1016/j.physa.2005.04.039).

Record type: Article

Abstract

A new method for the computation of flows at the micrometer scale is presented. It is based oil the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice Bhatnagar-Gross-Krook (ELBGK) is studied ill detail in order to quantify its relevance for microflow simulations. ELBGK is equipped with boundary conditions which are derived from molecular models (diffusive wall). A map of three-dimensional kinetic equations onto two-dimensional models is established which enables two-dimensional Simulations of quasi-two-dimensional flows. The ELBGK model is studied extensively in the simulation of the two-dimensional Poiseuille channel flow. Results are compared to known analytical and numerical studies of this flow in the setting of the Bhatnagar-Gross-Krook model. The ELBGK is ill quantitative agreement with analytical results in the domain of weak rarefaction (characterized by Knudsen number Kn, the ratio of mean free path to the hydrodynamic scale), up to Kn similar to 0.01, which is the domain of many practical microflows. Moreover, the results qualitatively agree throughout the entire Knudsen number range, demonstrating Knudsen's minimum for the mass flow rate at moderate values of Kn, as well as the logarithmic scaling at large Kn. The present results indicate that ELBM can complement or even replace computationally expensive microscopic simulation techniques such as kinetic Monte Carlo and/or molecular dynamics for low Mach and low Knudsen number hydrodynamics pertinent to microflows.

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Published date: 1 January 2006

Identifiers

Local EPrints ID: 49214
URI: http://eprints.soton.ac.uk/id/eprint/49214
ISSN: 0378-4371
PURE UUID: 63b04e20-1f37-460d-af36-68f404455861

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Date deposited: 24 Oct 2007
Last modified: 13 Mar 2019 20:54

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Contributors

Author: S. Ansumali
Author: I.V. Karlin
Author: C.E. Frouzakis
Author: K.B. Boulouchos

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