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Construction of lattice‐Boltzmann schemes for non‐Newtonian and two‐phase flows
Author(s) -
Vikhansky A.
Publication year - 2012
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.21664
Subject(s) - lattice boltzmann methods , collision , rheology , nonlinear system , boltzmann equation , constitutive equation , newtonian fluid , moment (physics) , algebraic number , mathematics , algebraic equation , lattice (music) , non newtonian fluid , statistical physics , classical mechanics , physics , mathematical analysis , computer science , mechanics , thermodynamics , computer security , quantum mechanics , finite element method , acoustics
In the present study we consider a general algebraically tractable approach to the construction of lattice‐Boltzmann (LB) schemes for the simulation of non‐Newtonian and two‐phase flows. The chain of moment equations is truncated at a level corresponding to the rheology of the liquid, and is closed by a Chapman–Enskog procedure. The collision term of the LB method is linked to the second moment of the velocity distribution via the constitutive equation of the liquid. The resulting nonlinear algebraic equation can be efficiently solved for an arbitrary rheological law. The algorithm can be extended to a two‐phase system.