Lattice Boltzmann simulation of flow in porous media on non-uniform grids

In this paper, the Lattice Boltzmann method (LBM) is adopted to simulate the incompressible flow in porous media on non-uniform grids. The flow through porous media was simulated by including the porosity into the equilibrium distribution function and adding a force term to the evolution equation to account for the linear and non-linear drag forces of the porous medium. Besides, non-uniform grids are adopted by using the interpolation-supplemented Lattice Boltzmann equation. Numerical simulations of lid-driven cavity flow, flow in a 2D symmetric sudden expansion channel, and cavity flow in polar coordinates are carried out. The results agree well with benchmark solutions, experimental data or traditional computational fluid dynamics method solutions. The present results demonstrate the potential of the Lattice Boltzmann algorithm for numerical simulation of fluid through porous media.