Simulations of fluid flow in porous media by lattice-gas and lattice-Boltzmann methods

Lattice-gas and lattice-Boltzmann methods can provide promising alternative approaches to traditional computational fluid dynamics. The geometric versatility of these methods makes them very attractive for simulating many complex systems, such as fluid flow in irregular geometries. Also, the inherent spatial locality of their updating rules makes these methods ideal for parallel computing. In this work, the basic ideas of these methods are first introduced. Then, many practical problems, such as boundary conditions, discretization errors, simulation time, and parallelization, are discussed, and a new efficient relaxation method, the Iterative Momentum Relaxation (IMR) method, is introduced. It is also shown that, with the Orthogonal Recursive Bisection (ORB) method, the performance of a parallel lattice-Boltzmann code can be significantly improved. Finally, several results of lattice-gas and lattice-Boltzmann simulations of single-fluid flow in 2D and 3D porous media are discussed. Simulation results for the tortuosity, effective porosity and permeability of a 2D random porous medium are reported. A modified Kozeny-Carman law is suggested, which includes the concept of effective porosity. This law is found to fit well the simulated 2D permeabilities. The results for fluid flow through large,3D random fibre webs are also presented. The simulated permeabilities of these webs are found to be in good agreement with experimental data. The simulations also confirm that, for this kind of materials, permeability depends exponentially on porosity over a large porosity range.