关于LBM做微尺度流动的疑问

luo@odu.edu

The credit is due to van Karman, who lived in the first half of last century. I don't see any reason why the credit should go to anyone else other than van Karman.

BTW, you jump from one subject to another. Now it is about credit. What does that have anything to do with the Knudsen number in LBE (where this all started)? Please get to the point -- don't shoot in bushes.

wdlxmzd

luo@odu.edu 发表于 2015-3-27 01:56
The credit is due to van Karman, who lived in the first half of last century. I don't see any reason ...

要说JUMP可能是您先的，本来简单的问题，饶来饶去的。
BTW，我再JUMP一下哈，您一直van Karman，很高端大气上档次，同时好像您很尊重他，请问您的论文里哪个地方 写了这个是van Karman关系，哪个地方引用了van Karman的工作？
年代已久，不引用情有可原，写个名字也行嘛，不写，普通读者以为您提出的，原创。

luo@odu.edu

"最后，本来就是正确的关系式，我何苦饶半天让人家初学者脑袋晕了，简单的回答，是。OK了"

Van Karman's relation is only valid to the Navier-Stokes equation, that is the point to be stressed. Moreover, something has been done long ago, and they ought not to be REINVENTED or REDISCOVERED.

However, in your response to the original question about validity of the LBE to simulate Knudsen flows, i.e.

"LBM是模拟N-S方程的，在进行常规的流动模拟时是利用Re来计算松弛时间的；而微尺度气体流动的特征参数是Kn，因而是通过Kn来确定松弛时间的，请问这样做合理吗？"

your answer was

"KN数与松弛因子相连，这个没有问题，因为松弛因子决定粘度，而KN数的定义可以与粘度联系起来。"

Which was misleading, if not outright erroneous, because, within the context, it suggests that the connection Kn and the viscosity (thus the relaxation rate) can somehow be effective to model or simulate Knudsen effects, which is simply not true.

Second, it appears that you cannot accept any criticisms to your comments. For example, in stead of pointing out what was wrong in my comments in terms of scientific/technical substance, you pointe to my paper, stating "KN数和松弛因子相连 之前微尺度LBM好像都是这样用的，您的论文好像也是这样用的", and citing my paper, which is neither factual nor true. In stead of attacking "people", you should focus on "subjects" -- substance of this discussion.

Please educate your audience, how can you us the LBE to model or capture the "flows in the transition regime", as claimed in the title of the following paper:

Li Q, He Y L, Tang G H, et al. Lattice Boltzmann modeling of microchannel flows in the transition flow regime. Microfluidics and nanofluidics, 2011, 10(3): 607-618.

Please explain to your audience first what "THE transition regime" is, and then why the approach in the above paper can solve this tough problem. Exhibit your scholarship and expertise on "flow in the transition regime", not your skills for street fighting, which have no place in this forum.

We are all looking forward to seeing your elucidation of "flows in transition regime" and your effective means or proposals to solve this problem, if you have any.

PS I would also suggest that you stick to "flows in transition regime" and do not deviate from the subject.

citadel

看到一篇paper，讲LBE和kinetic theory的联系，不知道是不是和这个topic相关

Exact Lattice Boltzmann Equation
http://journals.aps.org/prl/abst ... sRevLett.111.090601

luo@odu.edu

It is NOTHING to do with microflows and it is NOTHING more than a hoax. See the comment we wrote:

citadel

luo@odu.edu 发表于 2015-3-29 22:06
It is NOTHING to do with microflows and it is NOTHING more than a hoax. See the comment we wrote:

...

“the
conventional lattice Bhatnagar-Gross-Krook simulations of hydrodynamics belong to a parameter domain
which is disconnected from the kinetic theory domain.”
那他们的结论也是错的？

luo@odu.edu

Did they "prove" or substantiate their statement(s)? This would be a good exercise for you to find out the answer(s) yourself.

wdlxmzd

luo@odu.edu 发表于 2015-3-27 14:18
"最后，本来就是正确的关系式，我何苦饶半天让人家初学者脑袋晕了，简单的回答，是。OK了"

Van Karman's ...

我再说一次，跟之前我回答楼主的一样。

其一，采用KN数修正模拟过渡区，不是LBM专利，您学校，老道明大学的同事Ali Beskok，也是您合作的对象：
Luo (PI) and Beskok (Co-PI): A unifed modeling approach for micro- and nano-scale gas flows. NSF DMS-0807983, 07/01/2008-06/30/2011, $256,000.

有本专著，Microflows and nanoflows，其中介绍了什么是过渡区，Ali Beskok也介绍了他们提出的一种模拟过渡区的粘度修正方式，这种方式在这篇论文中应用了。Li Q, He Y L, Tang G H, et al. Lattice Boltzmann modeling of microchannel flows in the transition flow regime. Microfluidics and nanofluidics, 2011, 10(3): 607-618.

其二，LBM里采用修正粘度模拟过渡区，最早可能是ZHANG YH老师做的，
Capturing Knudsen layer phenomena using a lattice Boltzmann model
YH Zhang, XJ Gu, RW Barber, DR Emerson
Physical Review E 74 (4), 046704

07，08年郭老师采用粘度修正模拟过渡区微尺度：
n extended Navier-Stokes formulation for gas flows in the Knudsen layer near a wall
ZL Guo, BC Shi, CG Zheng
Europhysics Letters 80 (2), 24001

Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow
Z Guo, C Zheng, B Shi
Physical Review E 77 (3), 036707

我相信您至少跟Beskok和郭老师很熟，也肯定看过他们的论文。采用KN数修正模拟过渡区，不是某一个人的专利，更不是LBM的专利。您如果觉得自己不懂这一块，请您联系您的朋友Beskok或郭老师，跟您解析。
--------------------
最后，我想说的是，如果您真的是因为没看过上面的论文，而不知道他们做过，请您有时间的时候读读文献，也不带什么偏见，因为听说您只要看作者名字就知道论文水平，所以我估计这导致您很多文献都不屑于去看。

一叶障目，以至于很多不知道。所以您如果要问问题，请把文献读全，把来龙去脉搞清楚，搞清楚起源在哪，应该找谁去问。

我也算凑合回答了您的问题，请您回到我的问题，您的论文里写了那个是Van Karman关系式否？引用了否？这个时候您跟我提CREDIT属于Van Karman，然而在您的论文中死活找不到任何提及之处？

luo@odu.edu

Here is my direct response.

We do NOT cite van Karman in our JCP paper, nor did we claim credit for it, nor did we attribute the van Karman relationship to anyone who does NOT deserve the credit. Given the fact that the relationship is so trivial to derive once it is known, does this infringe van Karman's credit in any fashion or form? I will let others to judge.

In the past, I have mentioned "von Karman" relationship in my lectures repeatedly. And the only reason I pointed out that the relationship is due to van Karman is in response to your attribution of it to Professor ZL Guo. What is the basis for that? Are you going to admit your misstep?

You have no compunction to provide misinformation and erroneous assertions to public, especially those in need of help. What give you such confidence? And your only defence to other's criticisms is "You did it, too".

Are you saying that "模拟过渡区的粘度修正方式" can indeed solve the problems in transition region? Why? Sounds like another magic, at least the way you put it.

I can see that you are trying very hard digging, and if you keep trying,  you might get some there some day. You start to gain my admiration.

You seem to know a lot about what I have said. It would be helpful if you could provide a COMPLETE quote of what I said -- I trust you have reliable sources. I do not mind to open a discussion about how to read papers. With 25 years of experience and I am still reading papers every day, I certainly have something to say:

No. 1: NOT to trust something just because it has been printed (published);
No. 2: NOT to trust something just because it is well cited;
No. 3: You should have a black list of authors/papers which are untrustworthy;
  .....

wdlxmzd

luo@odu.edu 发表于 2015-4-4 14:29
Here is my direct response.

We do NOT cite van Karman in our JCP paper, nor did we claim credit f ...

在我看来，只要是认真做的，而非恶意剽窃，造假，抄袭等的工作，都是值得尊敬的工作。如果一个领域有恶意造假的人，那应该列进黑名单。可如果都是认真工作的，何来黑名单？尊重他人的工作，如同尊重自己的工作，即使你不认同。

认同不认同属于自我范畴，你不认同的， 不代表别人不认同，你不认同的，不代表最终学科发展就是这样的选择。每个人都不能 更没有资格去代替学科选择。那是科学发展的自身法则决定。

学科的发展，有引领型，有跟踪型，有推进型；跟踪已有工作，属于跟踪型。

科学研究其本身就是在 信任与质疑的平衡中发展，每个人都是这样，它必须信任一些东西，也必须在信任的过程中，怀疑一些东西。任何一个研究都必须建立一定的基础上。
如果什么都不信 什么都怀疑，那则如同陷入历史虚无主义，最终只能是灾难。

lhzhu

LBM做微尺度主要有两条途径，其一是你楼主说到对松弛时间的修正。但是我发现很多这方面的模型都是基于简单的拟一维问题提出了的修正关系式。算例验证也都是简单的直管道流。很少有看到对真正二维问题的细致的算例验证。
      另一条途径是是采用更多的离散速度点，如基于高阶赫尔米特展开的高阶LBM （参考J.P. Meng 和 Y.H. Zhang等人的工作）。但是这时离散速度空间和物理格子空间解耦了，失去了LBM碰撞、迁移这种计算方便的优势，需要采用有限体积或者有限差分计算。另外，随着展开阶数的变高，其计算结果收敛会变得非常地慢，还不如抛弃使用赫尔米特多项式零点做离散速度点这种做法，直接在速度空间布点（速度空间网格）。这样的话，实际上已经变成了离散速度法（DVM）了，看不到LBM的任何痕迹了（没有了碰撞迁移，没有了特殊选取的离散速度集）。

luo@odu.edu

"在我看来，只要是认真做的，而非恶意剽窃，造假，抄袭等的工作，都是值得尊敬的工作。如果一个领域有恶意 ...[/quote]


Just to be clear: you seem to be saying that so long as someone is "serious", sincere, hard-pushing, virtuous, honest, ..., then his/her work deserves respect.

Once again, we have to agree that we disagree. I never discuss anything about persons, I am solely interested in the technical merits of a work and nothing beyond. You seem to be very confused with person and work. It is latter we should talk about and not the former.

My black list includes charlatans  (persons falsely claiming to have a special knowledge or skill; a fraud), and their misguided, confused followers.

Not too long ago, you were trying very hard to lecture me that the MRT-LBE does NOT has any basis in kinetic theory, while the lattice BGK model has. No one questioned your sincerity, seriousness, honesty, but, does your virtuous personalities make your statement true?

Regarding van Karman relationship, you insisted that "这个关系式06年郭老师的文献了就严正推导过了". If it was given by van Karman some long time again, why do we need someone to "严正推导" again? Just because you seriously, sincerely believe so? What are we talking about here?!

luo@odu.edu

wdlxmzd 发表于 2015-4-3 13:49
我再说一次，跟之前我回答楼主的一样。

其一，采用KN数修正模拟过渡区，不是LBM专利，您学校，老道 ...

Mr. WDLXMZD,

You have been very good to avoid hard questions. It does not mean they can be avoided.

You definitely and confidently assert that "KN数与松弛因子相连，这个没有问题，因为松弛因子决定粘度，而KN数的定义可以与粘度联系起来" WITHOUT any qualifications, and that is what I disagreed.

Since you believe that "KN数与松弛因子相连，这个没有问题", please tell us how to simulate a 2D problem in transitional region: a cylinder placed in an arbitrary location inside a straight channel, i.e., a cylinder in the Poiseuille flow. Please show us how to do this with your scheme based on "KN数与松弛因子相连".

If you know how to do it, tell us how; if not, admit it -- it is not a shame to be ignorant, but, it is to pretend not.

lhzhu

LBM能不能算好过渡区，感兴趣的可以找个稍微复杂点的二维算例直接算一下就知道了。

比如算滑移区和过渡区的低速方腔流，这里我建议两个工况(Kn=0.075, Kn=1)，并附上DSMC的计算结果。

方腔边长L=1m作为特征长度. 上板拖动速度50m/s。所有壁面温度为273K, 并且Maxwell漫反射处理。腔内介质是 Agron（单原子气体）。粘性与温度的关系采用硬球分子模型。按上面的参数和分子模型假设，设置初始密度，可以调节Kn。下面给出Kn=0.075和Kn=1的竖直中心线和水平中心线上的速度profile （有量纲）.

=========== Kn=0.075, Y - U=====================
Y                                       , U
1.0000000000000000e-02, -1.6615250262250001e+00
2.6610169491525400e-02, -2.1196679286811899e+00
4.3220338983050798e-02, -2.4652098779492202e+00
5.9830508474576299e-02, -2.8431644632319300e+00
7.6440677966101697e-02, -3.1149379112006099e+00
9.3050847457627095e-02, -3.3795668964807599e+00
1.0966101694915301e-01, -3.5896106349303198e+00
1.2627118644067800e-01, -3.8732670594023499e+00
1.4288135593220300e-01, -4.0570608320640300e+00
1.5949152542372899e-01, -4.2776766930341097e+00
1.7610169491525399e-01, -4.5435175820392901e+00
1.9271186440678001e-01, -4.7310846884643700e+00
2.0932203389830500e-01, -4.9127294292296204e+00
2.2593220338983100e-01, -5.0971575290428603e+00
2.4254237288135599e-01, -5.2914088358683600e+00
2.5915254237288099e-01, -5.4809570606721598e+00
2.7576271186440698e-01, -5.6155820946636998e+00
2.9237288135593198e-01, -5.7770456854616503e+00
3.0898305084745797e-01, -5.9791926042799304e+00
3.2559322033898302e-01, -6.1829551173885902e+00
3.4220338983050802e-01, -6.2982830951624802e+00
3.5881355932203401e-01, -6.4663208506006402e+00
3.7542372881355901e-01, -6.5954070983434896e+00
3.9203389830508500e-01, -6.7065938014428701e+00
4.0864406779661000e-01, -6.7814255880030903e+00
4.2525423728813599e-01, -6.8460223300382603e+00
4.4186440677966099e-01, -6.8968399515372703e+00
4.5847457627118599e-01, -6.9761130383039198e+00
4.7508474576271198e-01, -6.9376446374482903e+00
4.9169491525423697e-01, -6.9463581483304804e+00
5.0830508474576297e-01, -6.9184916575014297e+00
5.2491525423728802e-01, -6.8323399918165704e+00
5.4152542372881396e-01, -6.6814661184454698e+00
5.5813559322033901e-01, -6.5454899196559202e+00
5.7474576271186495e-01, -6.4002250474491396e+00
5.9135593220339000e-01, -6.1228332720938896e+00
6.0796610169491505e-01, -5.7249179316224899e+00
6.2457627118644099e-01, -5.3421544942752597e+00
6.4118644067796604e-01, -4.9427404447007000e+00
6.5779661016949198e-01, -4.3495362168354896e+00
6.7440677966101703e-01, -3.7233947793701998e+00
6.9101694915254197e-01, -3.0511942817845998e+00
7.0762711864406802e-01, -2.1903024159693798e+00
7.2423728813559296e-01, -1.2257851481273401e+00
7.4084745762711901e-01, -2.3872403015470500e-01
7.5745762711864395e-01,  9.4134733799869996e-01
7.7406779661017000e-01,  2.1831952864744002e+00
7.9067796610169505e-01,  3.6176519023920002e+00
8.0728813559322099e-01,  5.2072219098199000e+00
8.2389830508474604e-01,  6.9046765843498203e+00
8.4050847457627098e-01,  8.7864315408600007e+00
8.5711864406779703e-01,  1.0702308821562101e+01
8.7372881355932197e-01,  1.2919650122474600e+01
8.9033898305084702e-01,  1.5256644159884900e+01
9.0694915254237296e-01,  1.7747975518547001e+01
9.2355932203389801e-01,  2.0471681096233201e+01
9.4016949152542395e-01,  2.3487659735211501e+01
9.5677966101694900e-01,  2.6779081161288001e+01
9.7338983050847505e-01,  3.0335086525335502e+01
9.8999999999999999e-01,  3.4684955741253098e+01


===========Kn=0.075,  X- V=====================
X                                       ,  V
1.0000000000000000e-02,  3.6519108820946400e+00
2.6610169491525400e-02,  4.6516148316479899e+00
4.3220338983050902e-02,  5.3729161796654799e+00
5.9830508474576299e-02,  6.0237914578278300e+00
7.6440677966101697e-02,  6.4567470335118804e+00
9.3050847457627095e-02,  6.8174688232841198e+00
1.0966101694915301e-01,  7.0586114569061698e+00
1.2627118644067800e-01,  7.2510591561564901e+00
1.4288135593220300e-01,  7.3826107331033999e+00
1.5949152542372899e-01,  7.3893547726762199e+00
1.7610169491525399e-01,  7.3709258555564299e+00
1.9271186440678001e-01,  7.3001798809565903e+00
2.0932203389830500e-01,  7.1779910605964599e+00
2.2593220338983000e-01,  7.0169017592729404e+00
2.4254237288135599e-01,  6.8100041720961402e+00
2.5915254237288099e-01,  6.5907505187547502e+00
2.7576271186440698e-01,  6.2213819221728803e+00
2.9237288135593198e-01,  5.9147786683162602e+00
3.0898305084745797e-01,  5.5288188735736501e+00
3.2559322033898302e-01,  5.1368698250165004e+00
3.4220338983050902e-01,  4.7574808361536203e+00
3.5881355932203401e-01,  4.3192703087618698e+00
3.7542372881355901e-01,  3.8778900390744999e+00
3.9203389830508500e-01,  3.4110622672961202e+00
4.0864406779661000e-01,  2.9453939440889201e+00
4.2525423728813599e-01,  2.4460262818397598e+00
4.4186440677966099e-01,  1.9929480350154400e+00
4.5847457627118599e-01,  1.4798535354691000e+00
4.7508474576271198e-01,  9.3487311058993505e-01
4.9169491525423697e-01,  4.5922242223075299e-01
5.0830508474576297e-01, -2.6072423223168800e-02
5.2491525423728802e-01, -6.1255777623895402e-01
5.4152542372881396e-01, -1.1386725709345900e+00
5.5813559322033901e-01, -1.6230352730488800e+00
5.7474576271186395e-01, -2.0989670619982399e+00
5.9135593220339000e-01, -2.6230274911225999e+00
6.0796610169491505e-01, -3.1456997850294801e+00
6.2457627118644099e-01, -3.5380650951828501e+00
6.4118644067796604e-01, -4.0611696900639496e+00
6.5779661016949198e-01, -4.5318389859321098e+00
6.7440677966101703e-01, -4.9183437188866099e+00
6.9101694915254197e-01, -5.3928133755474903e+00
7.0762711864406802e-01, -5.7647452822510301e+00
7.2423728813559296e-01, -6.1361379346938696e+00
7.4084745762711901e-01, -6.4101625175401198e+00
7.5745762711864395e-01, -6.7547939260631802e+00
7.7406779661017000e-01, -7.0065711152452401e+00
7.9067796610169505e-01, -7.2293765308836999e+00
8.0728813559321999e-01, -7.3507365591768501e+00
8.2389830508474604e-01, -7.4413484920823603e+00
8.4050847457627098e-01, -7.5045114639903998e+00
8.5711864406779703e-01, -7.4845050052012203e+00
8.7372881355932197e-01, -7.3642221911310104e+00
8.9033898305084702e-01, -7.1619533078396698e+00
9.0694915254237296e-01, -6.9066624758596298e+00
9.2355932203389801e-01, -6.5599584218593696e+00
9.4016949152542395e-01, -6.1243922115649303e+00
9.5677966101694900e-01, -5.5336539403223002e+00
9.7338983050847505e-01, -4.7265535543495201e+00
9.8999999999999999e-01, -3.7334784044311200e+00


===========Kn=1,  Y- U=====================
Y,                                         U
1.0000000000000000e-02, -2.6794531312042902e+00
2.6610169491525400e-02, -3.1228098245509699e+00
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===========Kn=1,  X- V=====================
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9.8999999999999999e-01, -5.5653327306652702e+00

luo@odu.edu

lhzhu 发表于 2015-4-11 14:29
LBM能不能算好过渡区，感兴趣的可以找个稍微复杂点的二维算例直接算一下就知道了。

比如算滑移区和过渡 ...

One has to be very careful to do the comparison.

There are in fact some results for cavity flow with a wide range of Knudsen number obtained using LBE and other methods. However, these comparison are inconclusive.

Correct and benchmark quality solution is crucial and necessary element for a conclusive comparison. To conduct conclusive comparison, one must demonstrate convergence. The DSMC results usually has errors in proportion to 1/sqrt{N}, where N is the particle number PER CELL. Thus, the DSMC data can be used for qualitative comparison, but not quantitative one.

To define a set of benchmark problems is yet to be done, but needs to. In fact, one can obtained very very accurate results for 1-D problems (Couette and Poiseuille flows), which come be used for benchmark purpose.

Above all, we need to understand the problems we are solving, i.e. we need a priori analysis.