Analytical Solution for the Lattice Boltzmann Model Beyond Naviers-Stokes (Advances in Applied Mathematics and Mechanics, 2021)
To understand lattice Boltzmann model capability for capturing non-equilibrium effects, the model with first-orderexpansion of the equilibrium distribution function is analyticallyinvestigated. In particular, the velocity profile of Couette flows is exactlyobtained for the D2Q9 model, which shows retaining the first orderexpansion can capture rarefaction effects in the incompressiblelimit. Meanwhile, it clearly demonstrates that the D2Q9 model is notable to reflect flow characteristics in the Knudsen layer.