Rigorous Navier–Stokes limit of the lattice Boltzmann equation

Abstract

In this article, we rigorously investigate the diffusive limit of a velocity‐discrete Boltzmann equation which is used in the lattice Boltzmann method (LBM) to construct approximate solutions of the incompressible Navier–Stokes equation. Our results apply to LBM collision operators with multiple collision frequencies (generalized lattice Boltzmann) which include the widely used BGK operators.