Multiscale LBM Simulations

Abstract

For flow problems of the continuum regime, the lattice Boltzmann method (LBM) is a good alternative to the traditional CFD solvers based on the N–S-like equations. It is efficient in modeling dynamic problems and very powerful for pore-scale applications, where the simulation of interface dynamics on the real irregular pore surface is challenging, if not impossible, to most of the traditional CFD solvers. We start in this chapter with the basic LBM algorithm to show its correlation with the N–S equation through the Chapman–Enskog expansion. Then, the widely used Shan–Chen model will be introduced to simulate multiphase multicomponent flow systems, having its applications detailed in the subsequent sections. We also present the extension of LBM to the Darcy-scale simulations, where the LBM works as a unified framework for simulations at different scales, i.e., both pore and Darcy scales, and the detailed results are given at the end of this chapter. In the ordinary application of LBM for computing the absolute permeability, we clarify the prevailed confusion interpreted as viscosity-dependent permeability and reveal the underlying rarefaction mechanism that has been commonly oversighted. Additionally, we also discuss the application of large eddy simulation of turbulence in the LBM framework and the same idea can be extended to model non-Newtonian fluids.