THERMAL LATTICE BOLTZMANN IN TWO DIMENSIONS

Diogo Nardelli Siebert (), Luiz Adolfo Hegele (), Rodrigo Surmas (), Luís Orlando Emerich Dos Santos () and Paulo Cesar Philippi ()
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Diogo Nardelli Siebert: Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Luiz Adolfo Hegele: Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Rodrigo Surmas: Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Luís Orlando Emerich Dos Santos: Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Paulo Cesar Philippi: Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 04, 546-555

Abstract: The velocity discretization is a critical step in deriving the lattice Boltzmann (LBE) from the Boltzmann equation. The velocity discretization problem was considered in a recent paper (Philippi et al.,From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models,Physical Review E73: 56702, 2006) following a new approach and giving the minimal discrete velocity sets in accordance with the order of approximation that is required for the LBE with respect to the Boltzmann equation. As a consequence, two-dimensional lattices and their respective equilibrium distributions were derived and discussed, considering the order of approximation that was required for the LBE. In the present work, a Chapman-Enskog (CE) analysis is performed for deriving the macroscopic transport equations for the mass, momentum and energy for these lattices. The problem of describing the transfer of energy in fluids is discussed in relation with the order of approximation of the LBE model. Simulation of temperature, pressure and velocity steps are also presented to validate the CE analysis.

Keywords: LBE; thermal models; BGK; quadrature; 47.11.-j; 05.10.-a; 51.10.+y (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107010784

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