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Hydrodynamics beyond Navier-Stokes: the slip flow model.

Wahyu P Yudistiawan¹, Santosh Ansumali, Iliya V Karlin

¹School of Chemical and Biomedical Engineering, Nanyang Technological University, 639798 Singapore.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 4, 2008

Summary

This summary is machine-generated.

The nine-bit lattice Boltzmann (LB) model accurately approximates slip flow in hydrodynamics beyond continuum limits. This study validates the LB model as a self-consistent slip flow approximation for simulations.

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Area of Science:

Fluid dynamics
Computational physics
Kinetic theory

Background:

Lattice Boltzmann (LB) models are increasingly relevant for hydrodynamics beyond the continuum limit.
Analytical solutions for nonlinear Couette flow highlight LB models' utility.

Purpose of the Study:

To systematically study the simplest LB kinetic equation (nine-bit model in 2D).
To quantify the nine-bit LB model as a slip flow approximation.
To extend analytical solutions to general shear- and force-driven unidirectional flow.

Main Methods:

Analytical solutions for nonlinear Couette flow.
Study of the nine-bit lattice Boltzmann kinetic equation in 2D.
Derivation of exact solutions for velocity and higher-order moments.

Main Results:

Exact solutions obtained for Couette and Poiseuille steady-state flows for all Knudsen numbers.
Quantitative agreement found between LB model results and Cercignani's slip flow solution.
The nine-bit LB model is validated as a slip flow approximation.

Conclusions:

The standard nine-bit LB model is a valid and self-consistent slip flow model.
LB models are suitable for simulations beyond the Navier-Stokes approximation.
This work quantifies the applicability of LB models in rarefied gas dynamics.