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Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria

Published online by Cambridge University Press:  01 June 2009

M. SBRAGAGLIA ,
R. BENZI ,
L. BIFERALE ,
H. CHEN ,
X. SHAN  and
S. SUCCI
M. SBRAGAGLIA*
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
R. BENZI
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
L. BIFERALE
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
H. CHEN
Affiliation:
EXA Corporation, 55 Network Drive, Burlington, MA 01803, USA
X. SHAN
Affiliation:
EXA Corporation, 55 Network Drive, Burlington, MA 01803, USA
S. SUCCI
Affiliation:
Istituto per le Applicazioni del Calcolo CNR, Viale del Policlinico 137, 00161 Roma, Italy
*
†Email address for correspondence: sbragaglia@roma.infn.it
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Abstract

Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria are placed within the framework of continuum kinetic theory. The mathematical treatment reveals that in order to be consistent with the correct thermo-hydrodynamical description, temperature must also be shifted, besides momentum. New perspectives for the formulation of thermo-hydrodynamic lattice kinetic models of non-ideal fluids are then envisaged. It is also shown that on the lattice, the definition of the macroscopic temperature requires the inclusion of new terms directly related to discrete effects. The theoretical treatment is tested against a controlled case with a non-ideal equation of state.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 299 - 309
Copyright
Copyright © Cambridge University Press 2009

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