Consistency study of Lattice-Boltzmann schemes macroscopic limit

Owing to the lack of consensus about the way Chapman-Enskog should be performed, a new Taylor-Expansion of Lattice-Boltzmann models is proposed. Contrarily to the Chapman-Enskog expansion, recalled in this manuscript, the method only assumes an su ciently 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, are 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.

G. Farag, S. Zhao, G. Chiavassa, Pierre Boivin. Consistency study of Lattice-Boltzmann schemes macroscopic limit. Physics of Fluids, American Institute of Physics, 2021, 33 (3), pp.037101. ⟨10.1063/5.0039490⟩. ⟨hal-03160898⟩

Journal: Physics of Fluids

Date de publication: 01-03-2021

  • G. Farag
  • S. Zhao
  • G. Chiavassa
  • Pierre Boivin

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