Fundamentals of Lattice Boltzmann Method

Different from the traditional computational fluid dynamics based on the macroscopic Navier–Stokes equations, the lattice Boltzmann method (LBM), which is considered as a special discrete format of the Boltzmann equation, has been rapidly developing since the 90s of the last century. In this chapter, we first discuss the hydrodynamics with motion description approaches at different scales. Then we give an introduction to the history of the LBM. On one hand, it originates from the lattice gas automata (LGA). On the other hand, it can be derived from the continuous Boltzmann equation. Finally, fundamentals of the LBM are introduced, including the most popular Bhatnagar-Gross-Krook (BGK) model, D2Q9 model for the two dimensions, boundary conditions like the non-equilibrium extrapolation scheme and so on.