Tutorial: Multi-Species Lattice Boltzmann Models and Applications

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Lattice Boltzmann solvers and applications Simplified kinetic models Andries-Aoki-Perthame (AAP) model The full Boltzmann equations for gas mixtures are much more formidable to analyze than the equation for a single-species system [3, 4, 5, 6]. A popular approach is to derive simplified model Boltzmann equations which are more manageable to solve. Numerous model equations are influenced by Maxwell’s approach to solve the Boltzmann equation by using the properties of the Maxwell molecule and the linearized Boltzmann equation [12]. The simplest model equations for a binary mixture is that by Gross and Krook [13, 12], which is an extension of the single-relaxation-time model for a pure system — the celebrated Bhatnagar-Gross-Krook (BGK) model. Many other models exist: Sirovich [14, 15], Hamel [16, 17], ... Pietro Asinari, PhD (Politecnico di Torino) Multi-Species LB Models Rome, Italy, on July 5-9, 2010 12 / 51
Lattice Boltzmann solvers and applications Basic consistency constraints Andries-Aoki-Perthame (AAP) model 1 The Indifferentiability Principle, which prescribes that, if a BGK-like equation for each species is assumed, this set of equations should reduce to a single BGK-like equation, when mechanically identical components are considered, i.e. the single fluid description should be recovered [18]. 2 The relaxation equations for momentum and temperature should be as close as possible to those derived by means of the full Boltzmann equations [19]. 3 All the species should tend to a target equilibrium distribution which is a Maxwellian, centered on a proper macroscopic velocity, common to all the species. 4 The non-negativity of the distribution functions for all the species should be satisfied. 5 A generalized H theorem for mixtures should hold. Pietro Asinari, PhD (Politecnico di Torino) Multi-Species LB Models Rome, Italy, on July 5-9, 2010 13 / 51
Page 1 and 2: Tutorial: Multi-Species Lattice Bol
Page 3 and 4: Outline of this tutorial 1 Kinetic
Page 5 and 6: Kinetic theory of rarefied gas mixt
Page 11: Lattice Boltzmann solvers and appli
Page 15 and 16: 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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