Consistency study of Lattice-Boltzmann schemes macroscopic limit

Abstract

Owing to the lack of consensus about the way Chapman–Enskog should be performed, a new Taylor-expansion of lattice-Boltzmann models is proposed. In contrast to the Chapman–Enskog expansion, recalled in this manuscript, the method only assumes a sufficiently small time step. Based on the Taylor expansion, the collision kernel is reinterpreted as a closure for the stress-tensor equation. Numerical coupling of lattice-Boltzmann models with other numerical schemes, also encompassed by the method, is shown to create error terms whose scalings are more complex than those obtained via Chapman–Enskog. An athermal model and two compressible models are carefully analyzed through this new scope, casting a new light on each model's consistency with the Navier–Stokes equations.