Tutorial: Multi-Species Lattice Boltzmann Models and Applications

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Abstract of this tutorial The aim of this tutorial is to discuss a numerical scheme based on the Lattice Boltzmann Method (LBM) for gas mixture modeling, which fully recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged approximation [1]. The mixture-averaged approximation is used to express the molar concentration gradient by means of a Fickian expression and a proper diffusion coefficient, both designed in such a way to be consistent with the Maxwell-Stefan formulation only in some limiting cases. Unfortunately (a) this approximation yields to Fickian diffusion coefficients depending on both the fluid transport properties and the local flow and (b) it is not valid in general. The key idea for avoiding these problems is to start from a Bhatnagar-Gross-Krook-type kinetic model for gas mixtures, recently proposed by Andries, Aoki and Perthame [2] (the so-called AAP model). Pietro Asinari, PhD (Politecnico di Torino) Multi-Species LB Models Rome, Italy, on July 5-9, 2010 2 / 51
Outline of this tutorial 1 Kinetic theory of rarefied gas mixtures Full Boltzmann equations Exchange relation for momentum 2 Lattice Boltzmann solvers and applications Single-relaxation-time Lattice Boltzmann scheme Andries-Aoki-Perthame (AAP) model LBM formulation by variable transformation 3 Validation and simple applications Pietro Asinari, PhD (Politecnico di Torino) Multi-Species LB Models Rome, Italy, on July 5-9, 2010 3 / 51
Page 1: Tutorial: Multi-Species Lattice Bol
Page 5 and 6: Kinetic theory of rarefied gas mixt
Page 11 and 12: Lattice Boltzmann solvers and appli
Page 29 and 30: Validation and simple applications
Page 33 and 34: Main loop Validation and simple app
Page 45 and 46: Conclusions In the present tutorial
Page 47 and 48: References II [7] C. Cercignani The
Page 49 and 50: References IV [17] B. B. Hamel. Two
Page 51: References VI [27] P. Asinari and T

Tutorial: Multi-Species Lattice Boltzmann Models and Applications

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