Stability investigation of implicit parametrical schemes for the systems of kinetic equations

Systems of parametrical lattice Boltzmann equations (LBE's) are considered. The formulae for the apparent viscosity for the general representation of these systems is obtained by Chapman - Enskog asymptotic expansion on Knudsen number. Obtained expression represents viscosity as a function of t...

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Bibliographic Details
Published in:Journal of physics. Conference series 2017-11, Vol.929 (1), p.12032
Main Authors: Prokhorova, Elizaveta A, Krivovichev, Gerasim V
Format: Article
Language:English
Subjects:
Asymptotic series
Cavity flow
Flow stability
Kinetic equations
Mathematical analysis
Parameters
Physics
Viscosity
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Summary:Systems of parametrical lattice Boltzmann equations (LBE's) are considered. The formulae for the apparent viscosity for the general representation of these systems is obtained by Chapman - Enskog asymptotic expansion on Knudsen number. Obtained expression represents viscosity as a function of the relaxation parameter and parameter of the LBE's. Necessary stability conditions in form of inequalities are derived from the non-negativity condition of the apparent viscosity. The validity of the stability conditions are demonstrated by the solution of lid-driven cavity flow problem.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/929/1/012032