LBM是否成熟到工程应用?

donglbm

首先我是mechanical engineering 专业的工科学生, 大概半年前,因为所作项目的缘故,接触到LBM的流体计算方法,我考虑LBM纯粹偏向应用.由于刚接触LBM,可能问的问题比较低级,请见谅,也请大家不吝赐教.

我的研究对象是多组分(三种气体)单相(气态)混合流动,geometry是一个真空反应器(出口有真空泵),之前尝试用Fluent等软件做过模拟.后来经过计算,发现流体的Kn数偏大,属于介观方法的LBM应该是个不错的选择.

看了一些书和研究了公开的一些代码后,发现没有想象地复杂,于是自己也学着编了一些程序(lid-driven flow, flow developing in pipe),都是采用LBGK(单松弛)的方法,结果不错.于是开始试着应用到我的geometry(2D),先做单组分等温模拟,于是出现了一些问题.

我的流体入口Re数30左右,入口按速度入口(Zou-He),出口按压力出口(Zou-He)设置,壁面是bounce back,出口的密度和整个lattice的初始密度相同.松弛时间的处理是这样的:保持Re数,设定一个Lattice长度,再设定较小的入口速度(0.1),计算lattice粘度,再通过粘度计算松弛因子.结果发现计算收敛后,流动似乎不充分发展,出口速度非常小.我的解释是,因为我的入口是自南向北,遇到反应器上表面后流动向东发展,最后自北向南从出口流出,在碰撞迁移过程中,速度的方向发生了很大变化,也就是动量发生了很大变化,这样松弛因子较小时就会出现流动缓慢不充分发展的情况.不知这样理解对吗?

现有还有以下疑问在困扰我:
1. 在计算中发现松弛因子影响流动的计算结果, 越大流动发展越快,计算也越容易发散.我的疑问是松弛因子是否和Re对应?如果是,小雷诺数对应小的松弛因子,计算收敛了,流动还没有充分发展,这似乎与实际不符(我在Fluent试了同等条件下的模拟,和LBM的结果差别很大).如果不是,我在保证Re数和实际相同的情况下,通过调整lattice长度,入口速度,来获取一个大的松弛因子,这样流动可以充分发展,但发现出口有涡流产生(出口有压差时).我的问题如果我调整不同的松弛因子,得到不同的计算结果,到底是那个结果跟实际相符的结果?也就是说,我怎么知道哪个松弛因子才和我要模拟的现实相符呢(因为Re数都相同)?还有,LBM计算的速度,压力等值如何和实际对应,比如我在LBM获得的速度大小怎样对应到实际的速度值呢?

2.关于LBM压强和密度的理解:出口设置为压力出口,实际是指定了出口的密度值,经过试验发现,密度初值和出口的密度值,相差较大时,尤其是在Re数大的时候,计算很容易发散.我想知道,这个压力差到底和实际的压力差如何对应?LBGK模型解的是不可压流动方程,意味着整个流场中的密度值应该恒定,也就是压力值应该恒定,那是否意味着我无法实现出口存在一个类似真空泵一样的低压(这样会导致出口密度突变)?如果可以实现,我的压力差如何设置才能符合实际情况呢?

3.这两天在论坛中看到大家讨论MRT的方法,目前还没有深入了解MRT,我不知道相对于传统的LBGK的方法,MRT的方法优势在哪?MRT既然是更一般的LBM方法,和LBGK比较,它是否求解更一般的流动方程?它有限制条件吗,比如不可压流动?MRT是否更适合我呢?

4.最后一个问题, LBM是否能够模拟化学反应,比如气体和固体的表面化学反应?有相应的成熟的模型吗?

对于我学工科而言,LBM只是一种方法,用它来解决我的工程问题,我现在就想了解LBM是否真的已经成熟到能够很好的解决工程问题?我要对这条路怀有多大信心呢?

希望大家多多指点,在这里先感谢大家了,谢谢!

[ 本帖最后由 donglbm 于 2013-4-19 00:31 编辑 ]

luo@odu.edu

To your general question, whether the LBM is matured enough for engineering applications, the answer is YES, as far as the method is concerned. It has been proven to be a good second-order method. However, whether there is a good and matured software, that is a different question. You seem to mix these two questions together.

I will only address the question about MRT vs LBGK: LBGK scheme is only a special case of MRT-LBE. MRT-LBE can remove the numerical artifacts inherent to the LBGK scheme, some of which you are experiencing, as alluded in your message.

The LBM is only a CFD tool, i.e., it only solves Navier-Stokes equation and can only be extended into slip-flow region. It is NOT a solver for kinetic equations and thus is unsuitable for flows with moderate or large Knudsen number.

To master a "matured" method, it takes some time and effort. The advantage of LBM's simplicity has often in times become the enemy of its success -- people no longer spend sufficient time to understand the method.

-- LS Luo

[ 本帖最后由 luo@odu.edu 于 2013-4-25 03:41 编辑 ]

onesupeng

不同意罗老师的关于算法和软件那一段的辩论方式

一个人理论上是可以蹦到月球上的，实际上我们见到的人力气太小蹦起来初始速度不够快，所以我们没有见到谁蹦到月球上。同理，LBM理论上可以做任何事情，只是因为编程序的人没有做好，所以还不能真正替代实验应用于工程设计。

大家当玩笑看啊。。。

luo@odu.edu

As a methodology, the LBM has come a long way in terms of our theoretical understanding. However, it requires much more than that to have a "matured" CFD tool/software, and that's the way I tried to recast the question raised by "donglbm". Of course, I may have done so incorrectly. Here we see how a not so well framed question is answered unsatisfactorily, and then leading to something else.  

For any practical problem of engineering significance, software complexity of codes is always an issue. This is true for any numerical method, be it finite-volume (FV), or finite difference (FD), or finite element (FE). Just because FV is theoretically well understood does not mean that a package like FLUENT (which was used to compared with a home-made LBE code by donglbm) can be easily made. In fact, the technical content related to a specific numerical methodology is only a very small fraction in a "matured" CFD solftware package like FLUENT. It is entirely inappropriate, in my opinion, to compare FLUENT with any home-made LBE code (or any home-made codes based on any method).

Now, I am quite intrigued by your example that "一个人理论上是可以蹦到月球上的". I would like to learn the "theory" which would allow a man to jump ( 蹦) to the Moon. Please enlighten and perhaps also entertain us.  This is indeed far more interesting that CFD (or LBE and such not).

[ 本帖最后由 luo@odu.edu 于 2013-4-26 20:50 编辑 ]

donglbm

罗老师,
您好,首先很感谢您的回复.我这两天拜读了您的关于MRT的两篇大作(文章真的很棒,很严谨,特别是Numerics of the lattice Boltzmann method这篇,个人非常喜欢).我也据此开始尝试写MRT的程序了.有几个关于MRT的问题想再请教您:
1.您提到的LBGK的"numerical artifacts"指的是什么?MRT如何消除这些”artifacts”的呢?
2.我不太理解大家说的"LBM是解不可压缩方程的人工压缩方法",我是这样理解,因为由LBM推导出的NS方程是可压缩方程,只不过是被用于求解不可压缩流(推导过程要求小Ma数).这样理解对吗?如果这样,那么是不是矛盾呢?因为推出的方程是可压缩,但推导时又使用了不可压的条件.
3. 在您的文章”Theory of the lattice Boltzmann method Dispersion, dissipation, isotropy, Galilean invariance, and stability”中,您没有由MRT推导NS方程,但提到MRT自然满足NS方程,那么我想知道MRT满足的是可压缩还是不可压缩NS方程(因为我看到有文章提到MRT导出的是可压缩NS方程)?
谢谢您的时间!

luo@odu.edu

Just to answer succinctly:

1) for simple fluids, the most prominent artifact is the tau-dependent boundary conditions (or viscosity-dependent, inaccurate boundary conditions, which have generated too many papers). This can be explicitly shown, and well understood, with analytic solutions for simple flows (I have published papers on this subject, and also have had heated debates with people on this bbs.)

2) LBE is "compressible" because it involves a variable density, and the (acoustic) wave speed in LBE is FINITE. However, LBE CANNOT handle shocks/discontinuities. It can be proved that LBE solves incompressible NS equation -- you can read the paper by Junk, Klar, and Luo (JCP, 2005).

3) There is no point to derive the NS equations from the LBE repeatedly. It is nothing more than a routine. You can try it.

Good luck.

[ 本帖最后由 luo@odu.edu 于 2013-4-28 02:00 编辑 ]

qingfengrumu

罗老师好，我也是刚刚开始学习LBM，我是学飞行器设计的，接触到的大部分问题是可压缩的。
我看到了很多让我迷惑的说法，有的说LBE是不可压的，有的文献又用LBE求解可压缩流场。是不是说基本的LBE是不可压的，如果要求解可压缩流场的话需要对模型进行一些修改？不知道我的理解是否正确。

uesoft

我不懂这些，只看到LBM是一种格子波尔兹曼方法，是一种粒子方法。粒子方法的特征很简单了。粒子方法一定是可压缩的，因为粒子速度可以变化，速度变化就意味着可压缩。据说LBM不需要网格，这也是个很大的优点，据说就是计算速度太慢。如果改进的话，也许LBM等粒子方法是CFD一种很有前景的方法，不过从计算速度来讲，可能有限体积还是快。

luo@odu.edu

The LBE is an "artificial compressibility" method. It is ONLY suitable for incompressible flows, i.e., Ma < 0.3, and without any shocks/discontinuities. It is "compressible" only because it allows density variations.

雪饮

LBM还是有一定局限的。而且主要偏向于微观。

luo@odu.edu

Whatever the limitations of the LBE, they have nothing to do with the "microscopic" origin --- the LBE is not a microscopic method and it is a CFD or macroscopic solver.

qingfengrumu

谢谢罗老师解答。我查到了好多文献，利用LBM计算高速流场，甚至是超音速，带激波的流动，MSC公司也推出了一款基于LBM方法的CFD求解器，也说能算超音速流动。当然，也有大量文献说LBM是不适于计算高速流动。所以我一直非常迷惑。

luo@odu.edu

Even if one can use the LBE to simulate high-speed flows, one has to ask the following questions:

a) Is the LBE accurate and efficient for high-speed flows?
b) does the LBE have any advantages over other methods?

Based on my experience, the answers to the above questions are both NEGATIVE.

-- LSL

雪饮

顶。