LBM方法的局限性

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请问LBM方法的局限性表现在哪些方面？它与SPH及传统的FVM、FDM方法相比有哪些优势?

周华

luo@odu.edu 发表于 2015-3-12 09:11
Since there is no misunderstanding of your intended "comparison" in my part, I may further conject ...

I just try to give a different viewpoint from an integral angle. Although LBM has some defects, it still is the most promising meshless method as I know.

luo@odu.edu

The advantages of LBE:
1) one of the BEST 2nd-order accurate method (if not the best), stress is also second-order;
2) easy to implement on a uniform mesh (perhaps the easiest);
3) ...

LBE is a finite-different (FD) method. SPH is more complicated and rather inaccurate. FVM is more complicated (reconstruction ...) but is on unstructured mesh. It is hard to say it in a few words.

周华

LBM方法在计算可压缩流动方面有限制，不过也有文章说LBM已经可以计算高马赫数流动。

周华

LBM另一个现实问题应该是计算量很大，做工程计算需要上百（甚至数百）个核的支持。最近两年GPU计算发展很迅速，给LBM的广泛应用提供了一个硬件基础。这些年LBM在国内快速兴起，一个原因是LBM方向上的顶尖专家大部分是在国外学习工作的中国人，国内LBM的兴起与他们的大力宣传有很大关系；另一个原因是LBM的基础理论是基于Boltzmann方程的，与分子动力学理论直接挂钩，比较容易发SCI文章，因而吸引了很多老师向这个方向转型。在整个CFD的版图上，FVM还是主流。

luo@odu.edu

周华 发表于 2015-2-8 12:18
LBM另一个现实问题应该是计算量很大，做工程计算需要上百（甚至数百）个核的支持。最近两年GPU计算发展很迅 ...

Dear Professor Zhou,

Thanks for your response. I was going to respond to your comment right away, but felt that it may require a more thoughtful response. If you don't mind, why do we start a serious discussion on the subject of LBE vs. other CFD methods?

This way the beginners may learn something.

Happy New Year!

-- L.-S. Luo

周华

luo@odu.edu 发表于 2015-2-27 12:07
Dear Professor Zhou,

Thanks for your response. I was going to respond to your comment right awa ...

罗老师，您好！现在刚好要开学了，讨论下这个问题可能时机正合适。我上面谈的是我个人对LBM方法的印象，不妥之处请您多多指教！

luo@odu.edu

周华 发表于 2015-2-8 12:18
LBM另一个现实问题应该是计算量很大，做工程计算需要上百（甚至数百）个核的支持。最近两年GPU计算发展很迅 ...

Dear Professor Zhou,

Thanks for your kind response. Let us restrict our discussion on the technical and scientific merits of the methods, and stay away from anything else.

So, the first issue is the computational cost of the LBE vs. other methods, as alluded in your comment. The LBE is essentially a central finite-difference (FD) method, thus it is a node based method. In contrast, finite-volume (FV) is a cell based one. In general, node based methods are LESS computational intensive than cell based methods, because cell based methods require the reconstruction to compute the fluxes at cell boundaries from the hydrodynamic variables at cell centers (nodes), while node based method do NOT have this step.

Specifically, the LBE requires less than 200 FLOPs per node in 3D (for the "D3Q15 model in 3D, which has 15 discrete velocities in 3D, the FLOP count is about 160; and for 2D models, it is even much fewer FLOPs).

How about FV method in terms of FLOPs?

周华

luo@odu.edu 发表于 2015-3-7 05:55
Dear Professor Zhou,

Thanks for your kind response. Let us restrict our discussion on the  ...

Well, I think it is not appropriate to discuss this problem on the basis of node-based or cell-based method. As I know, when LBM is applied to the computation of a flow field around a car, it is quite normal to use more than 100 computer nodes, but when a common FVM based software (with turbulence modelling like k-e/k-omega), like FLUENT/CFX etc., is used to do such simulations, usually not more than 10 computer nodes are enough. And this is why LBM software only take those big companies or institutes as their customers, because only such companies and institutes can afford to buy their software and the hardwares.

luo@odu.edu

You observed that black-box A using method X is far more computationally intensive than black-box B using method Y, therefore you conclude that method X must be more computationally intensive than method Y.

Am I correct in extracting this logic from your comment or not?

The purpose of this discussion is to dissect the methods in CFD, so a better understanding of all these methods can be attained. My hope is that this would benefit students.

周华

luo@odu.edu 发表于 2015-3-9 10:13
You observed that black-box A using method X is far more computationally intensive than black-box B  ...

Yes, you are correct, that is my logic. This is also a logic of an engineer, that is, when an engineer try to select a CFD software as his analysis tool, he usually will give it an evaluation first, on the performance, cost, efficiency etc., therefore his proposal can be expected to be approved by his manager. Even from the viewpoint of a CFDer, we must also evaluate the computational expense. For example, from a node-based or cell-based viewpoint, the intensity of LES method maybe equivalent  to that of a FVM method, but when we think about the amount of the mesh needed for LES, we can say it is still not suitable for most engineering applications.

luo@odu.edu

Since there is no misunderstanding of your intended "comparison" in my part, I may further conjecture and/or venture that the comparison may be fruitless because it may be made between oranges and apples (just to use the cliché).  

To do such a comparison meaningfully and fairly, one have no choice to conduct comprehensive evaluation of these black-boxes. Even so, one may still not be able to say anything about the kernel solvers in these black-boxes, the for kernels are only a (small) part in these black-boxes. Therefore, it is my view that such a comparison will not advance our understanding of the key techniques and technologies in CFD, and I have neither the capacity nor the interest in doing so.

Even though it is disappointing, we can only agree that we disagree, and that's it.

luo@odu.edu

Professor Zhou,

I have to differ again: the LBE is NOT a meshless method; it is merely a finite-difference method. It is this type of questions we need to clarity and elucidate.

So, let's talk about "meshless" method. The entire concept of "meshless" method rests on the idea of path-independent integration. Thus, one can construct meshless methods for Euler equations, but NOT for the Navier-Stokes ones. It is important to distinguish "particle" methods vs. "meshless" methods, which have been confused in the CFD community, sadly. The LBE may be qualified as a "particle" method (although I don't like that), but certainly not a "meshless" method.

webmaster

luo@odu.edu 发表于 2015-3-12 22:26
Professor Zhou,

I have to differ again: the LBE is NOT a meshless method; it is merely a finite-d ...

I think you are correct on this problem. While I first knew LBM, it was introduced as a meshless method, but when they show their results, they always presented it with a background mesh. If you fell something weired, LBMer will tell you this not a pure meshless method, but somehow it can be regard as a member of meshless method. "Particle method" tastes better.

周华

国内现在已经有人用LBM算超声速了,不过马赫数还不高 http://www.cnki.com.cn/Article/CJFDTotal-HKDI201303029.htm  发表于 昨天 11:37 IP:221.6.29.69 删除
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我记得看过一篇文章说LBM可以算马赫数等于100多的流动，不过后来我问过LBM方面的专家，他们说压缩性问题其实还没解决。所以，关键是什么叫“能算”，是把马赫数设置为100计算不发散，还是能比较真实地模拟高马赫数流动，其中的含义是不同的。