Lattice Boltzmann model for thermal transpiration

The conventional Navier-Stokes-Fourier equations with no-slip boundary conditions are unable to capture the phenomenon of gas thermal transpiration. While kinetic approaches such as the direct simulation Monte Carlo method and direct solution of the Boltzmann equation can predict thermal transpiration, these methods are often beyond the reach of current computer technology, especially for complex three-dimensional flows. We present a computationally efficient nonequilibrium thermal lattice Boltzmann model for simulating temperature-gradient-induced flows. The good agreement between our model and kinetic approaches demonstrates the capabilities of the proposed lattice Boltzmann method.