1 - A simple model of fluid mechanics

Summary

Although the microscopic makeup of fluids ranges from the simplest monatomic gas to, say, a complex mixture such as milk, nearly all fluids flow in a way that obeys the same equations of fluid mechanics. How simple can a model of a fluid be and still satisfy these same equations?

In this chapter we introduce a microscopic model of a fluid that is far simpler than any natural fluid. Indeed, it has nearly nothing in common with real fluids except for one special property—at a macroscopic scale it flows just like them!

This simple model represents an attempt to digitize, or reduce to logic, the equations of motion of hydrodynamics. After a discussion of the model's historical relation to other such attempts to simplify physics to make it more adaptable to computation, we consider some of the specific ramifications of the discovery of this simple fluid. This chapter establishes the context for the more detailed analyses, extensions, and applications of this model that follow.

The lattice gas

In 1986, Uriel Frisch, Brosl Hasslacher, and Yves Pomeau announced a striking discovery. They showed that the molecular, or atomistic, motion within fluids—an extraordinarily complicated affair involving on the order of 10²⁴ real-valued degrees of freedom—need not be nearly so detailed as real molecular dynamics in order to give rise to realistic fluid mechanics. Instead, a fluid may be constructed from fictitious particles, each with the same mass and moving with the same speed, and differing only in their velocities.