求教基本数学问题，如图

wdlxmzd

LBGK确实简单并且计算量小。优点缺点一向是分开谈，不能因为有了缺陷就不承认其优点，当然也不能因为其优点而忽视其缺陷。这也符合楼上对就是对，错就是错的观点。然PROF.LUO认为我们承认LBGK的优点是在自己欺骗自己，这一点我不敢苟同。

luo@odu.edu

Dear Wdlxmzd,

Well put, indeed. You have a scheme which is capable of computing WRONG results about 20% faster than a scheme which can compute correct results. So, we should emphasize that 20% gain in speed, and forget about the fact the results are WRONG.

Just in case you don't know what I am talking about, here is an example. For the 2D Poiseuille flow, which has a parabolic profile thus the LBE should yield the exact solution, because it is a 2nd-order scheme. Now, for the LBGK scheme, the channel width, which is a geometric feature of the flow, becomes viscosity-dependent. This problem becomes particularly severe in flows past porous media.

My question: Why should we care about computational speed if the answer is WRONG anyway?

-- LSL

[ 本帖最后由 luo@odu.edu 于 2011-3-30 10:07 编辑 ]

通流

这样的情况我也遇到不少。当你问为什么选取某种方法时，经常的回应是：
（1）简单，容易
（2）快
（3）某篇国外的论文是那样做的
（4）更奇怪的是，师兄是那样做的。

而最重要的应该总是：对的还是错的

wdlxmzd

感谢LUO老师的回复。
在ZOU/HE边界条件下，LBGK可以做到几乎100%的精度，也不会因为松弛因子出现viscosity-dependent。国内LBM们可以在郭老师早年黄皮书上边界条件一章看到相应的结果。如果研究的是直边问题，且雷诺数也不是很高，我个人觉得采用LBGK加ZOU/HE边界条件是一种好的处理方式。

对于LBGK+反弹式的边界条件，我认为这种可以消灭掉。对于高雷诺数问题，曲线边界，我非常赞同用MRT+相应的曲线边界处理。

[ 本帖最后由 wdlxmzd 于 2011-3-30 02:51 编辑 ]

luo@odu.edu

OK, LBGK + Zou-He BCs. Let's talk about that. I assume you use it for the Poiseuille flow and let's stick to it. Since Poiseuille flow is a linear flow with a second-order profile, the LBE, which is a second-order accurate scheme, should be able to yield the solution EXACTLY. So, why only  "几乎100%的精度"? If its solution "不会因为松弛因子出现" viscosity-dependence, why you need to limit to the cases where "雷诺数也不是很高"? What about the Stokes case, in which the Re=0 or almost 0?

Again, I have yet to see one single justifiable or defensible "advantage" of the LBGK model based on science. But through this discussion I do learn more and more about its "advantages" outside the realm of science.

luo@odu.edu

Dear "通流",

Thanks for your insight.

When I was little, whatever to be done had to be done to fit the mantra of "多，快， 好， 省", and we know the consequences of that (or maybe we don't?).  Back then everything was politicized and the end results matter little.

What deeply disappointed me is that the same thing is happening now in the realm of "science" in China. Trivial technical issues can be blown out of proportion and become non-scientific issues, as we have witnessed in this discussion board.

I was asked by some of my colleagues to join this board to answer students' questions and I never expected to get into this kind of senseless "discussions". But I am not surprised, given the pitiful and pathetic situation in the country.

Best,

-- LSL

[ 本帖最后由 luo@odu.edu 于 2011-3-30 20:19 编辑 ]

onesupeng

看着大家的讨论我都好激动。罗老师全盘否认LBGK我觉得也不太客观。当然，随着数值技术的进一步发展，它将会消失，这也是毫无疑问的。

目前来说，MRT的适用范围更广泛，精度更好一些。当然它也逃不出所有计算方法的命运，因为它也是一个工具。但是我觉得更重要的是，如何从最基本的物理背景出发，来构造这个“工具”，并用这个工具来对周围的事物进行研究开发等。

最后，很多人问我，为什么做LBM的那么多中国人。我发现确实很多中国人在做。不太明白为什么。

wdlxmzd

LUO老师，对于Poiseuille flow，LBGK + Zou-He BCs可以达到100%的精度。这个我最初学习LBM的时候编过程序，刚才也看了程序，实际上郭老师书上表述的结果也是100%的精度，例如，对于中间点，无量纲的应该是1.0，LBGK + Zou-He BCs可以精确达到1.0没有问题。

另外我说的，没有viscosity-dependence，是针对反弹边界在可以运行时，随着松弛因子的不同出现不同的误差，而LBGK + Zou-He BCs在可以运行时不会这样，并不是指LBGK + Zou-He BCs能够逃脱LBGK的固有缺陷。

另外，我们非常感谢您在百忙中回答论坛上的问题。

[ 本帖最后由 wdlxmzd 于 2011-3-30 15:17 编辑 ]

wdlxmzd

onesupeng

实际上这就是我们国内环境所造成的蝗虫般的科研行为，我们处于其中，受其害，却因为我们自己实在太渺小，难以改变。以前看到过相应的总结，特引述如下：
-------------------------------------------------------------------------------------------------
　　于是，在发表论文的压力下，加上中国人天生的勤奋和有空就钻的极强能力，如果国际上出现了一个新的学科方向，我们就会蝗虫一般地涌上，先把所有的简单问题全部做了，尽量不给外国人再留什么空间；接着，我们中国人就会在各个可能的应用领域把这个（或这些）方法全部应用一遍，或者其中也有一些新的意思包含在里面，但是基本就是“简单推广+简单应用”。

　　产生了这样的三个情形：

　　1，西方的学者发明了“镰刀”，我们迅速把直线型镰刀变成弯月型、三角型、四方型，倒弯月型，等等

　　2，西方的学者发现了一块长庄稼的新地。我们迅速召集人马，蝗虫一般地把这块地的没有被收割的部分在最短的时间内全部干掉。

　　3，西方学者发明了适合割某种庄稼A的“镰刀”，我们立刻把镰刀用在另外的庄稼地B，C，D上。期间也可能改造一些镰刀。

　　这样，所有的新学科方向只要出现，就立刻出现中国学者们蝗虫一般的身影。
----------------------------------------------------------------------------------------------------

通流

我也是经过一段时间以后才明白的事情。我们国家的学术水平，科技水平不高的主要原因是风气问题。具体的学术问题，只要环境，风气能够改进，提高是很快的，很可能一两年的时间。学术环境的培养，则是需要较长时间的努力。不是有一两个诺贝尔的人就能改变的。很多方面，那些50年代的海龟，也负有一定的责任。他们不是有意的，只不过没有努力去改变那样的状况。

我现在特别觉得毛主席选集中的一些话还是不错的：
（1）天下就怕认真两字，共产党就最讲认真。
（2）理论联系实际
（3）具体问题，具体分析（所谓的马克思主义活的灵魂）

什么叫认真？在学术上，就是学风问题，就是严谨。
怪不得现在有人怀念毛泽东。当然，他做的和说的并不一致。

luo@odu.edu

I assume the LBGK + Zou-He BCs you are talking about in the paper by Zou and He, Phys. of Fluids 9(6):1591-8 (1997). If so, you are wrong again. The analytic solution is given in the paper, and it is tau-dependent.

Sure you may come up with more examples. However, before you do so, please try the following. For the Poiseuille flow, you ought to get analytic solution from whatever LBE model you are using, which is easy to do, to educate and inform yourself before you make any claims.

luo@odu.edu

The problem I see is not just in the academia in China. It appears to me that the people as a whole has no spine anymore. Reason, justice, and conscience are not the spiritual pillars of this nation. This is best reflected in its educated class (we no longer have an intellectual class, just to be sure) which is completely rotten and corrupted -- it is no more than an interested party in the system. Thus, it is no surprise that they publish trashes and justify for doing so, because publishing is a means to making a better living, and better living they do make!  To speak of "Science" is vain under the circumstance.

luo@odu.edu

I only wish you could do solid work on "简单推广+简单应用" -- plenty of work needs to be done. Have you heard "V&V", i.e., validation and verification, which in my view falls into the category of  "简单推广+简单应用".

The LBE papers published in China I have seen most often are repetitive, erroneous, and even pirated.

luo@odu.edu

I don't know how to be objective ("客观"?) -- all I could do is some mathematical proof.

As to why so many Chinese are doing LBE, my observation is the following. We have a few very clever and savvy Chinese LBGK promoters, who know exactly how to exploit the autocratic system in China, which is very efficient and effective when it comes to decide what it wants to do, plus 1.3 billion people most of whom think 9x9 matrices are too hard to handle, and yet still want to do "science" to improve their lives. Only a very small fraction of 1.3 billion is needed to saturate a field.

As to whether the LBGK model should be abandoned or not, it depends what you are looking for. If it can improve your life in some way, why should you give it up? Keep it, by all means.

What is most impressive to me is that some many young people have devote so much effort to such an inconsequential subject.

[ 本帖最后由 luo@odu.edu 于 2011-3-31 21:07 编辑 ]

通流

这个牢骚越来越大了。所以我就不继续跟了。

不过你的那番对国内搞LBM方法的人比较多的议论可是有所指的啊。
听说有一位私底下把自己跟钱学森相比。