ABSTRACT
Lattice Boltzmann (LB) methods are relatively new, yet simple methods for simulating single and multiphase ˆuid behavior and are particularly suitable for porous media with irregular geometries. In this chapter, we brieˆy discuss the fundamentals of the single-phase LB method and its extensions to multiphase ˆuid systems. In particular, we discuss the merits of an earlier Shan−Chen-type model that was successfully used by us to simulate liquid water retention and wicking in a glass bead system. Although this model can reach excellent results, a ghost phase must be used in this model to generate phase separation. Additional drawbacks are that many simplifying assumptions must be made with regard to the domination of capillary forces over inertial, viscous, and gravitational forces and that the model type does not
CONTENTS
12.1 Introduction ................................................................................................ 328 12.2 LB Simulations ........................................................................................... 329
12.2.1 A Brief History ............................................................................... 329 12.2.2 The Single-Phase BGK LB Model ................................................330 12.2.3 Pressure, Gravity, and Flow .........................................................334 12.2.4 Phase Separation ............................................................................334 12.2.5 Extending the Shan-Chen Model with van der Waals
Equations of State........................................................................... 337 12.2.6 Implementation of Solid Phase ....................................................342
