Understanding of gas flows through porous media in the rarefied regimes is of tremendous importance in engineering applications such as shale gas extraction, microelectromechanical systems (MEMS) and air filtration devices. The lattice Boltzmann method (LBM) has several advantages for the simulation of gas flows through porous media, namely, (1) its explicit and local numerical scheme, which makes it massively parallelizable, and (2) its simple Boolean encoding of fluid and solid phases through a simple Cartesian grid. The LBM has been shown to be second-order convergent in space in the continuum regime. However, there is some disagreement in the literature on the convergence order of the LBM rarefied flow scheme, with some studies asserting a second-order convergence, while a first-order convergence was reported in others. In this presentation, it is shown that the scaling change from a quadratic relationship of the time step to the grid size $(\delta_t \sim \delta_x^2)$ in the continuum regime to a linear relationship $(\delta_t \sim \delta_x)$ is responsible for the degradation of the convergence order in the rarefied flow scheme for the LBM.

This is joint work with David Vidal, Sébastien Leclaire and François Bertrand. Financial support from the Simulation-based Engineering Science (Génie Par la Simulation) program funded through the CREATE program from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.