Application of Taylor series expansion and least square based lattice Boltzmann method to simulate porous media flow problems

In this study, 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 explicit Taylor series expansion and least square based lattice Boltzmann method (TLLBM). 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 of the standard LBM. Numerical simulation of lid-driven cavity flow is carried out. The results agree well with existing data in the literature. The present results demonstrate the potential of the Lattice Boltzmann algorithm on non-uniform grids for numerical simulation of fluid through porous media

کلیدواژه ها:

Taylor series expansion and least square based lattice Boltzmann method ، flow through porous media ، non-uniform grids