FLUID FLOW SIMULATION IN MICROPOROUS MEDIA ON NONUNIFORM GRIDS USING THE TAYLOR SERIES EXPANSION AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD

摘要

In this study, the lattice Boltzmann method (LBM) has been applied for the first time to simulate incompressible flow in microporous media on nonuniform grids. The flow through porous media is 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 nonlinear drag forces of the porous medium. Besides, nonuniform grids are adopted by using the explicit Taylor series expansion and least squares-based lattice Boltzmann method (TLLBM). The TLLBM is based on the standard LBM with an introduction of the Taylor series expansion and the least squares approach. The final equation is an explicit form and essentially has no restriction on mesh structure and lattice model. Since the Taylor series expansion is only employed in the spatial direction, the time accuracy of this method remains the same as the standard LBM. In order to validate the LBM code, at first, a lid-driven cavity flow in porous media is simulated and the obtained results are compared with the data existing in the literature. Then, the proposed method is applied to simulate a lid-driven cavity flow in microporous media for different Darcy and Knudsen numbers. The present results demonstrate the potential of the lattice Boltzmann algorithm on nonuniform grids for numerical simulation of fluid flow through porous media.