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Simplified lattice Boltzmann method for non‐Newtonian power‐law fluid flows
Author(s) -
Chen Zhen,
Shu Chang
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4771
Subject(s) - lattice boltzmann methods , non newtonian fluid , power law fluid , newtonian fluid , power law , statistical physics , mathematics , boundary value problem , mechanics , mathematical analysis , physics , statistics
Summary In this paper, we present a simplified lattice Boltzmann method for non‐Newtonian power‐law fluid flows. The new method adopts the predictor‐corrector scheme and reconstructs solutions to the macroscopic equations recovered from the lattice Boltzmann equation through Chapman‐Enskog expansion analysis. The truncated power‐law model is incorporated into this method to locally adjust the physical viscosity and the associated relaxation parameter, which recovers the non‐Newtonian behaviors. Compared with existing non‐Newtonian lattice Boltzmann models, the proposed method directly evolves the macroscopic variables instead of the distribution functions, which eliminates the intrinsic drawbacks like high cost in virtual memory and inconvenient implementation of physical boundary conditions. The validity of the method is demonstrated by benchmark tests and comparisons with analytical solution or numerical results in the literature. Benchmark solutions to the three‐dimensional lid‐driven cavity flow of non‐Newtonian power‐law fluid are also provided for future reference.