FROM THE BOLTZMANN TO THE LATTICE-BOLTZMANN EQUATION: BEYOND BGK COLLISION MODELS

Paulo Cesar Philippi (), Luiz Adolfo Hegele (), Rodrigo Surmas (), Diogo Nardelli Siebert () and Luís Orlando Emerich Dos Santos ()
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Paulo Cesar Philippi: 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
Diogo Nardelli Siebert: 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

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 04, 556-565

Abstract: In this work, we present a derivation for the lattice-Boltzmann equation directly from the linearized Boltzmann equation, combining the following main features: multiple relaxation times and thermodynamic consistency in the description of non isothermal compressible flows. The method presented here is based on the discretization of increasingly order kinetic models of the Boltzmann equation. Following a Gross-Jackson procedure, the linearized collision term is developed in Hermite polynomial tensors and the resulting infinite series is diagonalized after a chosen integerN, establishing the order of approximation of the collision term. The velocity space is discretized, in accordance with a quadrature method based on prescribed abscissas (Philippiet al.,Phys. Rev E73, 056702, 2006). The problem of describing the energy transfer is discussed, in relation with the order of approximation of a two relaxation-times lattice Boltzmann model. The velocity-step, temperature-step and the shock tube problems are investigated, adopting lattices with 37, 53 and 81 velocities.

Keywords: Lattice Boltzmann equation; thermal models; multiple relaxation times; 47.11.-j; 05.10.-a; 51.10.+y (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107010796

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