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2007•International Journal of Modern Physics CRequires access

A TWO-FLUID BGK LATTICE BOLTZMANN MODEL FOR IDEAL MIXTURES

C. Pico, Luís Orlando Emerich dos Santos, Paulo César Philippi

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Abstract

In the present work, a lattice Boltzmann model for binary mixtures is formally derived from a two-fluid kinetic model of Maxwell molecules by discretizing the Boltzmann equation. In this model, collisions among the same and different species are treated separately, as non-linear BGK terms, enabling the independent management of the fluid viscosities and the binary diffusion coefficient. The velocity space is discretized, in accordance with a quadrature method based on prescribed abscissas. A Chapman-Enskog analysis is performed for deriving the macroscopic mass and momentum transport equations. The model is verified against theoretical solutions for the concentration and velocity step problems.

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What this paper is about

In the present work, a lattice Boltzmann model for binary mixtures is formally derived from a two-fluid kinetic model of Maxwell molecules by discretizing the Boltzmann equation. In this model, collisions among the same and different species are treated separately, as non-linear BGK terms, enabling the independent management of the fluid viscosities and the binary diffusion coefficient. The velocity space is discretized, in accordance with a quadrature method based on prescribed abscissas. A Chapman-Enskog analysis is performed for deriving the macroscopic mass and momentum transport equations. The model is verified against theoretical solutions for the concentration and velocity step problems.

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Available abstract

In the present work, a lattice Boltzmann model for binary mixtures is formally derived from a two-fluid kinetic model of Maxwell molecules by discretizing the Boltzmann equation. In this model, collisions among the same and different species are treated separately, as non-linear BGK terms, enabling the independent management of the fluid viscosities and the binary diffusion coefficient. The velocity space is discretized, in accordance with a quadrature method based on prescribed abscissas. A Chapman-Enskog analysis is performed for deriving the macroscopic mass and momentum transport equations. The model is verified against theoretical solutions for the concentration and velocity step problems.

Key concepts: Lattice Boltzmann methods, Discretization, HPP model, Boltzmann equation, Bhatnagar–Gross–Krook operator, Statistical physics, Binary number, Work (physics)

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