Abstract

The first part of this introduction is devoted to the known derivation of the lattice Boltzmann method (LBM): We track two different derivations, a historical one (via lattice gas automata) and a theoretical version (via a discretization of the Boltzmann equation). Thereby the collision term is approximated with a single relaxation time model (BGK) and we motivate the introduction of this common approximation. By applying a multiscale expansion (Chapman-Enskog), the solution of the numerical method is verified as a meaningful approximation of the solution of the Navier-Stokes equations. To state a well posed problem, common boundary conditions are introduced and their realization within a LBM is discussed.

In the second part, the LBM is extended to handle coupled problems. Four cases are investigated: (i) multiphase and multicomponent flow, (ii) additional forces, (iii) the coupling to heat transport, (iv) coupling of electric circuits with power dissipation (as heat) and heat transport.