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Appendix: Chapman-Enskog Expansion in the Lattice Boltzmann Method
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In this article, the authors used the Chapman-Enskog expansion in the lattice Boltzmann method (LBM) to derive a Navier-Stokes-like equation and obtained a formula to correlate the LBM model parameters to the kinematic viscosity implicitly implemented in LBM simulations.Abstract:
The Chapman-Enskog expansion was used in the lattice Boltzmann method (LBM) to derive a Navier-Stokes-like equation and a formula was obtained to correlate the LBM model parameters to the kinematic viscosity implicitly implemented in LBM simulations. The obtained correlation formula usually works as long as the model parameters are carefully selected to make the Mach number and Knudsen number small although the validity of Chapman-Enskog expansion that has a formal definition of time derivative without tangible mathematical sense is not recognized by many mathematicians.read more
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Dissertation
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References
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Journal ArticleDOI
Lattice BGK Models for Navier-Stokes Equation
TL;DR: In this article, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order approximation with a properly chosen equilibrium distribution, with a relaxation parameter that influences the stability of the new scheme.
Journal ArticleDOI
Lattice boltzmann model for the incompressible navier-stokes equation
Xiaoyi He,Li-Shi Luo,Li-Shi Luo +2 more
TL;DR: Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented and are found to be in excellent agreement with theory.
Journal ArticleDOI
An Alternative Scheme to Calculate the Strain Rate Tensor for the LES Applications in the LBM
Jun Li,Zhengwei Wang +1 more
TL;DR: In this article, the strain rate tensor, Sij, used to determine the eddy kinematic viscosity can be calculated from the second-order moment of the nonequilibrium distribution function, and the current total nondimensional relaxation time can be determined explicitly.