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A Practical Introduction to the Lattice Boltzmann Method

A Practical Introduction to theLattice Boltzmann MethodAlexander J. WagnerDepartment of PhysicsNorth Dakota State March 20082 Contents1 Introduction72 The Boltzmann equation93 Derivation of Introduction .. The Boltzmann equation .. The BGK approximation .. Moments of the equilibrium distribution function .. Mass conservation .. Momentum conservation .. Energy conservation .. 134 Lattice The Lattice Boltzmann equation .. Taylor expansion .. One dimensional implementation .. Isothermal Lattice Boltzmann .. Non-ideal fluids .. Boundaries .. 225 Applications of Lattice Turbulence .. Liquid-gas systams.

10 CHAPTER 2. THE BOLTZMANN EQUATION Solving these equations for a, bα and cwe find that the equilibrium distribution is given by f0 = n (2πθ)3/2 exp − (v−u)2 2θ (2.7) which is known as the Maxwell-Boltzmann distribution.

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