Lattice Boltzmann Methods for Fluids, Plasmas, and Quantum Systems

流体流动现象通常用以Navier和Stokes命名的复杂方程来描述，这些方程将流体视为连续的、无限可分的介质，或者用基于这些方程的计算机程序来描述。然而，真正的流体是由分子组成的，每个分子的行为都遵循牛顿的运动定律。牛顿定律比纳维-斯托克斯方程简单得多，但是分子数量太多了，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代替了少数复杂的方程。晶格玻尔兹曼方法占据了中间立场：这些方程每一个都只比牛顿定律复杂一点，但只比已经存在于纳维-斯托克斯方程中的多一些。这种中间立场被证明是非常富有成效的，即使是在模拟可以用纳维-斯托克斯方程描述的现象时，通过保持与牛顿分子定律的联系，人们可以深入到纳维-斯托克斯方程不再适用的更小的长度尺度。现在，越来越小的技术设备，即所谓的微电子机械设备，通常可以达到这些尺度。

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.