Analytical solution for the lattice Boltzmann model beyond Naviers-Stokes

To understand lattice Boltzmann model capability for capturing nonequilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer

Multiscale lattice Boltzmann approach to modeling gas flows

For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different theoretical frameworks. In particular, it is not easy to recover the non-equilibrium information required by the kinetic method which is lost by the continuum model at the coupling interface. Therefore, we present a multiscale lattice Boltzmann (LB) method which deploys high-order LB models in highly rarefied flow regions and low-order ones in less rarefied regions. Since this multiscale approach is based on the same theoretical framework, the coupling precess becomes simple. The non-equilibrium information will not be lost at the interface as low-order LB models can also retain this information. The simulation results confirm that the present method can achieve model accuracy with reduced computational cost