Rigorous Navier–Stokes limit of the lattice Boltzmann equation

Article type: Research Article

Authors: Junk, Michael | Yong, Wen‐An

Affiliations: FB Mathematik, Universität Kaiserslautern, Erwin‐Schrödingerstraße, 67663 Kaiserslautern, Germany E‐mail: junk@mathematik.uni‐kl.de | IWR, Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany E‐mail: yong.wen‐an@iwr.uni‐heidelberg.de

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.

Keywords: lattice Boltzmann method, Navier–Stokes equation, multiple collision frequencies, diffusive scaling, stability, incompressible limit

Journal: Asymptotic Analysis, vol. 35, no. 2, pp. 165-185, 2003