Diffusive and moisture transport in porous materials like ceramics, concrete, soils, and rocks plays an important role in many environmental and technological processes . For example, the service life and durability of concrete can depend on the rate of ingress of chloride ions while the diffusion of carbon dioxide controls the rate of carbonation of the cementitious matrix. Further, such processes depend on the degree of saturation of the porous medium. The detailed simulation of such transport phenomena, subject to varying environmental conditions or saturation, is a great challenge because of the difficulty of modeling fluid flow in random pore geometries and the proper accounting of the interfacial boundary conditions. In this paper, we will review  some recent advances in the modeling of fluid flow in complex geometries using the discrete Boltzmann methods. Discrete or lattice Boltzmann methods (LB) have emerged as a powerful technique for the computational modeling of a wide variety of complex fluid flow problems including single and multiphase flow in complex geometries. These methods naturally accommodate a variety of boundary conditions such as the pressure drop across the interface between two fluids and wetting effects at a fluid-solid interface. Since the LB method can be derived from the Boltzmann equation, its physical underpinnings can be understood from a fundamental point of view. Indeed, discrete Boltzmann methods serve as an ideal mesoscopic approach that bridges microscopic phenomena with the continuum macroscopic equations. Further, it can be directly implemented as a numerical method to model the time evolution of such systems. Finally, the LB method generally needs nearest neighbor information, at most, so is well suited to take advantage of parallel computers.
An outline of the paper goes as follows. After a brief review of the theory of the LB method, results are presented to validate predictions of fluid flow through a few simple pore geometries. Large scale simulations of fluid flow through a Fontainebleau sandstone microstructure, generated by X-ray microtomography, will then be presented. Single phase flow calculations were carried out on systems containing 5103 computational elements. We also calculate relative permeability curves as a function of fluid saturation and driving force. The next section describes solution of the Brinkman equation using a lattice Boltzmann based approach. Finally, a comparison of the performance of such codes on different computational platforms is presented.