Lattice Boltzmann Methods for Fluids, Plasmas, and Quantum Systems

流体流动中的现象通常由以Navier和Stokes命名的复杂方程来描述，该方程将流体视为连续的、无限可分的介质，或者由基于这些方程的计算机程序来描述。然而，真实的流体是由分子组成的，每个分子的行为都符合牛顿运动定律。牛顿定律比纳维尔-斯托克斯方程简单得多，但分子太多了，每立方厘米可能有10^18个分子，以至于人们用大量的简单方程取代了少数复杂的方程。格子玻尔兹曼方法占据了中间地带：每个方程都只比牛顿定律复杂一点，但它们只比纳维尔-斯托克斯方程中已经存在的多几个。这中间地带已被证明是非常富有成效的，即使是模拟现象，可以描述的Navier-Stokes方程，并通过保持接触牛顿定律的分子可以达到更小的长度尺度，在那里的Navier-Stokes方程不再足够。这些规模现在通常由更小的技术设备，即所谓的微电子机械设备来达到。

Phenomena in fluid flow are usually described by complicated equations named after Navier and Stokes that treat fluids as continuous, infinitely divisible media, or by computer programs based on these equations. However, real fluids are made up of molecules, each of which behaves according to Newton's laws of motion. Newton's laws are much simpler than the Navier-Stokes equations, but there are so many molecules, perhaps 10^18 per cubic centimetre, that one replaces a handful of complicated equations with vast numbers of simple equations.The lattice Boltzmann approach occupies the middle ground: the equations are each only a little more complicated than Newton's laws, but there are only a few more of them than are already present in the Navier-Stokes equations. This middle ground has proved very fruitful even for simulating phenomena that could be described by the Navier-Stokes equations, and by retaining contact with Newton's laws for molecules one may reach down into smaller lengthscales where the Navier-Stokes equations are no longer adequate. These scales are now routinely reached by ever smaller technological devices, the so-called microelectrical mechanical devices.