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Contents. 1.1 Preface 1.2 Overview 1.3 The basic idea of lattice-gas cellular automata and lattice Boltzmann models 1.3.1 The Navier-Stokes equation 1.3.2 The basic idea 1.3.3 Top-down versus bottom-up 1.3.4 LGCA versus molecular dynamics
Contents. 2.1 What are cellular automata? 2.2 A short history of cellular automata 2.3 One-dimensional cellular automata 2.3.1 Qualitative characterization of one-dimensional cellular automata 2.4 Two-dimensional cellular automata 2.4.1 Neighborhoods in 2D 2.4.2 Fredkin’s game 2.4.3 ‘Life’ ...
Contents. 3.1 The HPP lattice-gas cellular automata 3.1.1 Model description 3.1.2 Implementation of the HPP model: How to code lattice-gas cellular automata? 3.1.3 Initialization 3.1.4 Coarse graining 3.2 The FHP lattice-gas cellular automata 3.2.1 The lattice and the collision rules 3.2.2 Microdynamics of the FHP...
Contents. 4.1 The Boltzmann equation 4.1.1 Five collision invariants and Maxwell’s distribution 4.1.2 Boltzmann’s H-theorem 4.1.3 The BGK approximation 4.2 Chapman-Enskog: From Boltzmann to Navier-Stokes 4.2.1 The conservation laws 4.2.2 The Euler equation 4.2.3 Chapman-Enskog expansion 4.3 The...
Contents. 5.1 From lattice-gas cellular automata to lattice Boltzmann models 5.1.1 Lattice Boltzmann equation and Boltzmann equation 5.1.2 Lattice Boltzmann models of the first generation 5.2 BGK lattice Boltzmann model in 2D 5.2.1 Derivation of the Wi 5.2.2 Entropy and equilibrium...
Contents. 6.1 Boolean algebra 6.2 FHP: After some algebra one finds ... 6.3 Coding of the collision operator of FHP-II and FHP-III in C 6.4 Thermal LBM: derivation of the coefficients 6.5 Schläfli symbols 6.6 Notation, symbols and abbreviations
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