求教基本数学问题，如图

hellolegend

请指点！

luo@odu.edu

Assuming C = | vector{C} |, and vector{C} = (U, V, W), thus C = sqrt{U^2 + V^2 + W^2}, then you should just write down the integral and see whether they are equal or not.

Isn't this a question you should go back to check your textbooks of calculus with the definition of multi-dimensional integrals?

hellolegend

大概“对称性”表示U，V，W等价，因而上述3个积分相等。
谢谢Luo教授。

luo@odu.edu

May I asked some questions here?

Most questions I have seen on this discussion board are rather rudimentary. I wonder why they cannot be addressed in one's own environment and one has to come to internet for this kind of questions. What are those teachers and supervisors or mentors? Aren't they supposed to help their students?

I was a student sometime ago, and I still am for I don't know much. But I am at least competent enough to help my students.

wdlxmzd

从国内LBM领域本身来说，做LBM的学生，他们的导师很多都没有搞过LBM，同时，他们导师下面做LBM的学生极少，有时候只有他/她。

从大方面来说，国内学术界，绝大部分领域都是这样，国内绝大部分研究生都是自编自导自演。当然也有少数是例外的。

实际上很多LBM能做的，传统方法能做，而且做得很好。但为什么国内LBM会盛行呢，因为这个东西可以包装项目，有噱头，比较好忽悠项目，项目下来了，当然是学生做。然而大多数情况下，写项目申请的人根本不懂LBM，也不知道行不行得通。国内的学生苦啊。这个问题的解决恐怕如同台湾问题一样，目前只能承认现实，并维持现状。

luo@odu.edu

Dear Wdlxmzd,

Thank you very much for your honest and candid response to my inquiry, which I do appreciate. The dire situation you described only confirms my suspicion.  It is because of this intolerable situation which prompted me to express my dissent with those "experts" who have been by and large responsible for the LB fashion trend in China.

While agreeing in part with your assessment of the current situation in academia in China, I cannot entirely agree with your outlook and your general assessment about the LB method.

First, yes, we have to recognize the reality (承认现实), but by no means we have to MAINTAIN the status quo (维持现状). Students in China may not be able to do much to change the status quo, but in my position I do NOT have to go along with those "experts" in China. The least we can and should do is to tell the truth, and not to push the students into dark pits. For this reason, we are organizing the Spring School on LBM in Beijing (May 2-6). The students will hear the things countering the loud noises yelled by those "experts" in China. We do not expect to reverse the tide (or tsunami), that will take time and persistence.  But we believe this will make some difference -- even to a small number of students, it would be a gratification.

I also find your response in a sharp contrast with your comments about the LBGK scheme, which has been condemned and completely abandoned by many who work in the field and are serious.  Since you believe that "实 际上很多LBM能做的，传统方法能做，而且做得很好", then my question is, naturally, why have you invested your time in the LBM (assuming you have)?  One likely answer could be that it was not your choice but your mentor's (I could be wrong, of course). However, after having realized that "实际上很多LBM能做的，传统方法能做，而且做得很好", why are you still defending the LBGK scheme (or its existence) so vigorously? I use the word "defending" for I know no better word, and it is not meant to label you or offend you.

The question we ought to ask is not whether a method/scheme can do things very well or not, but which method/scheme is better for what and when. To this end, we have done some serious benchmarks to make the point. The point is not that some traditional methods can or cannot work very well, the point is at what cost and how versatile these methods can be.

There is another point I would like to discuss here. It's easy (or easier) to blame bosses or mentors -- most of them, if not all, are guilty as charged. But, what about students themselves?  The question asked in this particular discussion board is a basic calculus question concerning multi-dimensional definitive integrals and the concept of symmetry (对称性) and isotropy (各向同性), which have absolutely nothing to do with the LBM or kinetic theory particularly.  They are the most basic and fundamental concepts in physics and mathematics. While I have never been discouraged by those "experts" who are nothing  more than charlatans, however, I have been very much discouraged by  those students telling me linear algebra of 9x9 matrices are too hard to handle. Well, we can blame the entire dysfunctional education system in China ..., but that won't solve any problem for us, not soon anyway.

-- LSL

[ 本帖最后由 luo@odu.edu 于 2011-3-28 03:53 编辑 ]

wdlxmzd

感谢罗教授的回复。

我并不是LBGK的卫道者，正如您所说，“however, I have been very much discouraged by  those students telling me linear algebra of 9x9 matrices are too hard to handle” 换句话说，对很多国内初学者或入门者来说，MRT的使用特别是MRT的理论和模型构造，超出了他们的现状。

我想说的是，这并不表示国内初学者没有能力去学习和使用MRT。他们需要时间，可国内的学术环境和氛围，缺的就是时间。在巨大的外部压力促使下，速成或快速入门是唯一途径，否则，不要说去研究什么东西，就连来自导师的压力你都处理不好。当然，某些导师例外，但导师们也处在国内的环境中，他们自己在受到上面的压力，他们给学生的压力，无非是这种压力的传递而已，所以根源在大环境。

因此，在这样一个环境下，如果一个初学者根本搞不定MRT，那么在短时间内他能用的就只有LBGK了。在他有点成果可供汇报导师用后，就可以缓解他的外部压力，从而可以使他有比较宽松的环境去继续从事进一步的研究，也许他下一步从事的研究就是MRT。如果您说我在维护LBGK，那么这就是我从中国实际和中国国情出发维护LBGK的第一点。

第二点，在之前的贴子里面，我也说过。LBGK简单，这一点只是纯粹从数学上出发，不论及其他。那么因为它的简单，人们在研究LBGK的过程中，也许更容易发现了某些规律，如建模规律，而后将其拓展至MRT，这是一条可用的科研思路。也许您可以直接从MRT发现规律，但这样一条思路，给那些直接从MRT出发研究不了规律的人提供了一条曲线道路。实际上，根据很多论文，国内郭老师在研究一些问题时，也经常从这样一条思路去研究。

这就是我的根本观点。

luo@odu.edu

Dear Wdlxmzd,

You offer two arguments: (1) everyone is under pressure so they do what they do -- the LBGK scheme is the savior for everyone, because (2) it is simple.

You repeat your argument that  " 在研究LBGK的过程中，也许更容易发现了某些规律，如建模规律,"  I have begged you to offer me just one such example and so far I have seen none.

-- LSL

wdlxmzd

关于第二个问题，给个例子
郭老师等研究轴对称的理论时，先从圆柱坐标系的连续的BOLTZMANN-BGK方程出发发现了相应的理论或者说建模规律。Phys. Rev. E 79, 046708 (2009) Theory of the lattice Boltzmann equation: Lattice Boltzmann model for axisymmetric flows.

其后，他们又根据相关规律构建了相应的MRT模型
Multi-relaxation-time lattice Boltzmann model for axisymmetric flows
Liang Wanga, Zhaoli Guo, and Chuguang Zheng
Computers & Fluids
Volume 39, Issue 9, October 2010, Pages 1542-1548.

我在之前的贴子里面也表达了这样的意思，在动理论中没有MRT，因此从连续的BOLTZMANN-BGK方程出发时，LBGK模型几乎是必然，其后根据已有的单松弛构建多松弛是一条思路。最近也有学者将Shan-Chen的单松弛多相模型拓展至相应的MRT。
Phys. Rev. E 82, 046708 (2010) Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow

作为一种研究思路，我个人认为我的第二个观点是正确的，因为前人用过并正在用，且我自己也用过，有过体会。如果说MRT是最终目的，我想只要选择自己能够熟练驾驭的思路就可以了。

对于我的第一个观点，我想您的总结背离了我原本的意思。我没有用everyone ，也没有说LBGK是每个人的救星。如果有着宽松的学术环境和充足的时间，从一开始就研究比较深入的东西是可能的。

但国内的研究生们绝大部分完全没有这样的条件。即使是国内的青年学者，国内基金项目的每年考核，以及结题要求，压迫着他们，他们也很难获得宽松的学术环境。

因此，我比较赞成的是，从简单入手，取得成果（也许这些成果在外面看起来什么也不是），尽快缓解压力，从而争取到比较宽松的学术环境，为从事深入且需要时间的科研提供条件。

我们经常看到，国外的学生读好几年博士，也许中间一篇论文也没有，但最后积累到质变，做出成大成果。这样的情况在国内绝大部分高校和研究所都难以出现，因为如果长时间没有一点东西，就算万万幸导师不施加压力，毕业条件的硬性指标在那放着，自己都会被毕业压力给折磨死，更不要说去科研了。

[ 本帖最后由 wdlxmzd 于 2011-3-31 15:34 编辑 ]

wdlxmzd

我赞同并非常支持去传播MRT，TRT等的优势，但我所担心的是，如果在一边倒的趋势下，导致国内初学者不敢使用LBGK，不敢从BGK出发去研究问题，就会非常糟糕。

我也是一名学生，今年刚博士毕业，09年我参加了广州的ICMMES会议，说心里话，作为学生，那个会是我所有参加过的会中过得最压抑的一次。当您在台上说 I will tell you how stupid this method (LBGK)?
也许您没有考虑到这样会给下面使用BGK和造BGK模型的学生在会场带来多大的压力。

前不久，有个初学者问我要MRT的程序，他刚刚入门，说看MRT看得非常痛苦，也调不通，他跟我说，别人告诉他，LBM领域的大师PROF. LUO极不赞同LBGK，所以他想从MRT入手。我也是有导师的人，没有导师的授权，不能给别人传程序，所以我也帮不了他。

总体来说，我非常赞同去传播MRT，TRT，但从我自己所经历和所了解的中国实际国情出发，我坚持我的两个基本观点。

[ 本帖最后由 wdlxmzd 于 2011-3-31 15:35 编辑 ]

luo@odu.edu

Yes, I responded to you comment that "在动理论中没有MRT" -- it is false. The linearized Boltzmann equation with an infinite number of relaxation frequencies is the Gross-Jackson model, a generalization of the BGK model.

I can see that how painful for someone who has been addicted to the "LBGK" habit. You can keep it so long as you like. Just don't tell me that the LBGK model has technical advantages.

Based on your responses, it is amply apparent to me that if the LBGK model has advantage, it is not about science, it is about something else beyond science. Since the LBGK scheme is nothing more that an addiction for those helpless addicts, I don't see any reason not to eradicate it completely and entirely. Yes, taking away opium, alcohol, and drugs from addicts will cause pain to them, but it is not necessary a bad thing.

[ 本帖最后由 luo@odu.edu 于 2011-3-28 19:29 编辑 ]

wdlxmzd

我说动理论中没有MRT主要想表达的意思是，LBGK可以从动理论中的连续BOLTZMANN-BGK方程导出，而LBM-MRT却没有这样一个类似的过程。

LBGK简单，计算量小于MRT，这个是事实。

我想学术界应该允许百花齐放，允许各种科研思路 科研方法并存。就如同我们人一样，有的人孤僻孤傲不合群，有的人平易谦和合群，总不能把不合群的人给消灭掉吧。再比如，孤傲的人可能不适合在中国从事科学研究，会混不下去，因为中国国内环境就是那样，讲究很多微妙的东西，但并不表示这样的人不适合在美国从事科学研究。每个国家有每个国家的国情，每个人有每个人的选择。

另外，国内科研并来就不是纯粹的science。在国内，人们首先要维持基本生活，才能谈更高档的东西，才能追求发展。如果连活都活不下去，其他的都难以为继。对国内研究生来说，更是如此，缓解压力是国内研究生尤其是博士生的一门大学问。

有一位德高望重的老院士曾说过，在我们中国搞科研，国家往哪里投钱，我们就搞什么方向。这并不低俗，相反这是大彻大悟后的务实。如果论基本工资，国内绝大部分大学的副教授的基本工资大概也就4000多一点每个月。但城市里的房价却是1万元一平米的量级。在这样环境下，如何维持生活才是前提。

不好意思，扯偏了。您的基本意思我理解了。感谢您的回复。

[ 本帖最后由 wdlxmzd 于 2011-3-28 17:07 编辑 ]

luo@odu.edu

In my previous response to your comments, I have already stated that in my lectures for short courses given in ICMMES, I explicitly derived MRT-LBE from the continuous linearized Boltzmann equation (the Gross-Jackson model). I also said that I have NOT seen any LB models with kinetic under-pinning which cannot be DIRECTLY derived from continuous kinetic equations.

Yes, the LBGK schemes are about 20% faster purely based on FLOPS counts when compared with the corresponding MRT counterparts. Is that an advantage of the LBGK scheme?! Now we are really kidding ourselves.

Enough has been said. I have nothing to say about pseudo-science, nor do I have any thing to say about making a living by doing pseudo-science -- which is beyond my competence.

So long.

-- LSL

wdlxmzd

每个国家有每个国家的国情，即使中国情况再糟糕，那些也不能称为伪科学，毕竟大环境限制，如果说是伪科学，可能要侮辱中国数以千万计的科研工作者。

历史的发展总有个过程，中国的未来靠的就是这些搞“伪”科学的科研工作者和将要从事“伪”科学的研究生们。相信随着历史的发展，将来会慢慢变好。

通流

其实，对于科学问题，对就是对，错就是错。老是强调客观情况，并不是合适的做法，也是影响我国科研水平的大敌。

我不懂LBM，只是一般性的意见。