Lattice Gas Hydrodynamics (Relié)

Lattice gas hydrodynamics is the name used to describe the approach to fluid dynamics starting from a simple micro-world constructed as an automaton universe. In this universe, the microscopic dynamics is based not on a realistic description of interacting particles, but merely on the laws of symmetry and of invariance of macroscopic physics. We imagine point-like particles residing on a regular lattice, where they move from node to node and undergo collisions when their trajectories meet at the same node. If the collisions occur according to some simple logical rules, and if the lattice bas the proper symmetry, then the automaton shows global behavior very similar to that of real fluids. This book carries two important messages. First, it shows how an automaton universe with very simple microscopic dynamics - the lattice gas - can exhibit macroscopic behavior in accordance with the phenomenological laws of classical physics. Second, it demonstrates that lattice gases have spontaneous microscopic fluctuations that capture the essentials of actual fluctuations in real fluids. The two aspects are closely related, offering a microscopic approach to the description of fluid systems. Accordingly, the book follows the philosophy of classical statistical mechanics, and introduces the reader to the world of the discrete analogue of continuous molecular hydrodynamics. This book will be of interest to graduate students and researchers in statistical physics, computational physics, hydrodynarnics, applied mathematics and engineering.