关于LBM做微尺度流动的疑问

zjl

大家好，有几个问题向大家请教：
最近看了一些关于利用LBM做微尺度气体流动的文章，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？
还有，有学者通过对模型进行考虑努森层的修正，将LBM扩展到过渡区的流动模拟，这样做可以吗？
还请各位前辈指教，谢谢！

luo@odu.edu

My entire point is that the connection between Kn and the relaxation parameter WITHOUT careful qualifications is INCORRECT, period. The important qualification within the context is the van Karman relation, which limits the scope to the Navier-Stokes equations.

Also, I do not believe that a blanket statement WITHOUT careful qualifications is scientific, to say the least -- it won't help those who are seeking answers. And worse, it may mislead, and that is what I try to prevent.

wdlxmzd

zjl 发表于 2015-3-13 13:50
非常感谢罗老师的文章。
前面我所说的那些是从这篇文章里面看的，罗老师您看一下。
Li Q, He Y L, Tang ...

LBM做微尺度流动是LBM学术界本世纪前十年的美好愿望，最早起于CHEN SHI YI, NIU XIAODONG等人的工作，对于D2Q9，其本质等价于N-S+滑移边界；
过渡区工作最早应该是Capturing Knudsen layer phenomena using a lattice Boltzmann model
Yong-Hao Zhang, Xiao-Jun Gu, Robert W. Barber, and David R. Emerson
Phys. Rev. E 74, 046704 – Published 12 October 2006

郭老师等的08年关于过渡区的工作
Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow、Zhaoli Guo, Chuguang Zheng, and Baochang Shi
Phys. Rev. E 77, 036707 – Published 21 March 2008

上述论文都是D2Q9+KN数修正=N-S+KN数修正，所以你的问题哈，其实应该是问微尺度流动这个大学科，N-S+KN数修正 可行不可行，而不是LBM本身，LBM本身的D2Q9只是N-S的求解器。

N-S+KN数修正 这种处理方法被学者研究的时候，微尺度LBM可能还没产生。

有好多问题应该归纳出其本质，而非表象。

当然对于N-S+KN数修正能否做过渡区，答案肯定是既然是修正那肯定是经验的，近似的，不准确的。要做过渡区的微尺度，用DSMC好。

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We do NOT cite van Karman in our JCP paper, nor did we claim credit for it, nor did we attribute the van Karman relationship to anyone who does NOT deserve the credit.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;
  .....

luo@odu.edu

It has been PROVED that the LBE is a Navier-Stokes solver and NOT a kinetic solver. Thus, it can only model the so-called slip-flow flow region with very small Kn.

Of course, there are a lot CLAIMS (not proofs) made in contrary to the proof.

zjl

luo@odu.edu 发表于 2015-3-7 05:17
It has been PROVED that the LBE is a Navier-Stokes solver and NOT a kinetic solver. Thus, it can o ...

罗老师您好，非常感谢您的回答。但是有很多人通过对模型进行修正得到的结果（速度分布、压力分布等）和DSMC, linearized Boltzmann equation 的解有很好的一致性，这个该怎么理解呢？

luo@odu.edu

where did you see that the modified LBE and DSMC, linearized Boltzmann equation 的解有很好的一致性? Who claim that the LBE can capture the Knudsen layer? Any proof?

You may want to read my paper:

W. Li, L.-S. Luo, and J. Shen.
Accurate solution and approximations of the linearized BGK equation for steady Couette flow.
Computers & Fluids 111:18-32 (16 April 2015).

zjl

luo@odu.edu 发表于 2015-3-9 10:15
where did you see that the modified LBE and DSMC, linearized Boltzmann equation 的解有很好的一致性?  ...

非常感谢罗老师的文章。
前面我所说的那些是从这篇文章里面看的，罗老师您看一下。
Li Q, He Y L, Tang G H, et al. Lattice Boltzmann modeling of microchannel flows in the transition flow regime[J]. Microfluidics and nanofluidics, 2011, 10(3): 607-618.

zjl

wdlxmzd 发表于 2015-3-15 22:20
LBM做微尺度流动是LBM学术界本世纪前十年的美好愿望，最早起于CHEN SHI YI, NIU XIAODONG等人的工作，对 ...

对，您说的非常好，非常感谢您的解答。那只用来模拟滑移区流动的话，通过Kn来确定松弛时间，这样做合理吗？

wdlxmzd

zjl 发表于 2015-3-16 08:16
对，您说的非常好，非常感谢您的解答。那只用来模拟滑移区流动的话，通过Kn来确定松弛时间，这样做合理吗 ...

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。

zjl

wdlxmzd 发表于 2015-3-17 08:36
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。

恩，谢谢！
非常感谢您的解答！

luo@odu.edu

zjl 发表于 2015-3-13 21:50
非常感谢罗老师的文章。
前面我所说的那些是从这篇文章里面看的，罗老师您看一下。
Li Q, He Y L, Tang ...

You should ask the authors of the paper to explain their work.

Allow me just talk about the most basic concept in rarefied flows, i.e. the definition of the Knudsen number Kn, which is the ratio of the mean-free path and a macroscopic characteristic length.

In the LBE, the the grid spacing is basically the measure of the mean-free path -- imagine the the picture about how the mesh is refined. Consequently, the mean-free path cannot be defined in this way.

If one can indeed use the link between the viscosity and the mean-free path to DIRECTLY solve the kinetic equations, it is a free lunch, which is too good to be true. Because, if so, we can use the Navier-Stokes solver to solve kinetic equations.

wdlxmzd

luo@odu.edu 发表于 2015-3-23 02:25
You should ask the authors of the paper to explain their work.

Allow me just talk about the mos ...

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
F. Verhaeghe, L.-S. Luo, and B. Blanpain.
Lattice Boltzmann modeling of microchannel flow in slip flow regime.
Journal of Computational Physics 228(1):147-157 (January, 2009).
公式29下面好像是。

luo@odu.edu

Yes, we did (use the relationship between Kn and the viscosity). The key point is the von Karman relationship given by Eq. (2), which related Kn to both Ma and Re. Furthermore, we only claimed to solve the compressible, low-speed, isothermal Navier-Stokes equations, and we demonstrate the convergence.

Equation (29) and the ensuing discussion are our criticism about the lattice BGK model, and the faith based on it to claim the "Knudsen effects"; that is, we analysis the defects of the LBGK model and what has been sold as snake oil. It is NOT what we do nor what we promote.   

If the only point of an argument is  "You did it, too", then it won't be so convincing, is it?

I would urge those who are interested in the work to read the paper, and read it CAREFULLY.

wdlxmzd

luo@odu.edu 发表于 2015-3-25 03:34
Yes, we did (use the relationship between Kn and the viscosity). The key point is the von Karman rel ...

楼主问的两点：一是LBM里，KN与松弛因子相连，是否合适，我回答了是，我看您用英文回答的很详细，补充了一句您也是这么用的；二是，他问KN层修正来模拟过渡区是否合适，我回答大意这不是LBM的专利，是其领域已有的东西，被用到LBM里而已，LBM只是N-S 求解器而已。

wdlxmzd

luo@odu.edu 发表于 2015-3-26 01:06
My entire point is that the connection between Kn and the relaxation parameter WITHOUT careful quali ...

如果说现在的文献中其关系式是错的，我当然会详细回答。

这个关系式06年郭老师的文献了就严正推导过了，您论文中的所谓van Karman relation，即公式2在微尺度文献中早已出现过，那只不过是郭老师以及后来的大部分微尺度论文中所用KN与粘度关系式的无量纲参数表达而已。我希望您能秉承一个公正的立场，一个东西，同样形式，出现在自己论文 是正确的，是高端大气上档次的，出现在别人论文的就饶半天，扯BGK拉，扯N-S啦。我建议您还是看看其他学者的论文吧，别人也是MRT做的，别人也没说自己不是N-S求解器。

BTW. 我一直觉得您应该是个能和人合作的公正学者，因为您的大部分高引或者有意义的工作都是别人第一作者，这证明您一直推崇他人，而自己居后。

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。