Lattice Boltzmann Method

Macroscopic descriptions of porous media—porosity, permeability, capillary pressure—are not scale-free. They inherit the volumes and time intervals over which they were defined, and in shales and other highly confined systems that dependence can no longer be ignored. This book opens with an ontology of scales, introducing a Representative Elementary Time alongside the REV and a nonlocal view of constitutive laws. It then develops the lattice Boltzmann method as a mesoscopic bridge from molecular insight to continuum models. Chapters cover fundamentals, boundary treatments, and lattice-to-physical unit conversion; high-Knudsen-number flow and transport, nanoconfined adsorption, and their coupling for pure gases and CH4-CO2 and CH4-H2 mixtures in complex pore geometries; adaptive multiblock refinement and modern C++ implementation for large domains; and neural operators as fast surrogates for LB solvers. Worked MATLAB and C++ examples and an open-source solver accompany the text. Impact of confinement on the physics of fluids and simulation of transport, flow and adsorption of gases in confined and complex environments using the Lattice Boltzmann method. High-performance computing and multiblock methods.