罗老师对Karlin评论的回应

oceanwen

应该有助于大家对熵LBE的理解。

[ 本帖最后由 oceanwen 于 2012-10-15 11:47 编辑 ]

oceanwen

原始论文

[ 本帖最后由 oceanwen 于 2012-10-15 11:48 编辑 ]

oceanwen

Karlin的评论

[ 本帖最后由 oceanwen 于 2012-10-15 11:48 编辑 ]

lwd1981

看完了，觉得很有道理，呵呵
一直以来，我都对ELBM表示怀疑。本来LBM就等效于人工压缩方法，ACM需要采用双时间步长方法模拟非定常流动，而LBM中没有采用双时间步，本来就有误差，而ELBM还在计算过程中采用超松弛，在CFD领域中都应该知道只有内迭代才使用超松弛这些加速收敛和增强稳定性的方法，非定常的外迭代是不可以采用这些技术的，而LBM中没有双迭代一说，所以我个人认为ELBM对于非定常问题那就更加不准确了。至于定常问题，可能也有问题，我想问题可能主要是出现在边界层里面，ELBM通过改变局部松弛时间来达到稳定，实际上影响了局部的粘性，而在远离边界的地方可以看成是无粘的，松弛时间的变化几乎不会对局部流场产生较大影响，因此我认为在远离边界区域应该是正确的或者至少误差不显著，而在靠近边界附近肯定不会准确。
    一点浅见，希望罗老师和其他高人能够指点一二，呵呵

luo@odu.edu

One thing I must emphasize is this: do NOT take whatever in print or whoever's words (including mine, of course) on their face values. To be a scientist, one must have curiosity and thus questioning attitude. The most sever problem with the so-called ELBE scheme is that its viscosity is a function of space and time solely for the consideration of NUMERICAL stability and nothing else. Not only it is inaccurate near boundaries, it is also inaccurate in any regions where the flow fields undergoes severe variations.

Another thing I noticed is that very few can repeat the results by Karlin et al. and it is very hard to find the numerical implementation of the ELBE. I know why now, as I discussed in my Reply to KSC's Comment.

[ 本帖最后由 luo@odu.edu 于 2012-10-16 09:44 编辑 ]

lwd1981

“it is also inaccurate in any regions where the flow fields undergoes severe variations.”，我说的是定常情况，应该不至于吧。ELBM在远离壁面区域至多
相当于一个limiter，可能导致结果耗散大一点，不至于引起显著误差吧。非定常
问题另当别论，非定常问题由于有时间累积效应，可能影响较大吧，呵呵。
    一点粗浅理解，呵呵。欢迎指正！

luo@odu.edu

The way the ELBE works is to compute the distributions depending on the flow field. The more severe the flow fields vary, the stronger the damping is -- larger variations of flow fields result in larger deviation of the distributions from their equilibria, thus require large dissipation, especially in small scales. This point is crucial for direct numerical simulations (DNS) -- the ELBE can essentially wipe out all small scale dynamics. In this sense the ELBE is rather inaccurate, because it "smooths" flows. My comments are based on the principles of the ELBE.

For the 2D sheer flow [Minion, Brown, JCP, 138:734 (1997)], which has no boundary, the ELBE and LBGK schemes perform poorly [Dellar, JCP 190:351 (2003) ]. Of course, this is a time-dependent case, and we just don't have good examples of flows free of boundary and yet with flow fields vary severely.

[ 本帖最后由 luo@odu.edu 于 2012-10-18 07:58 编辑 ]

lwd1981

再次学习了，由衷地感谢罗老师的回复。看来ELBE如果用到FDLBM 或者FVLBM，耗散将更大，误差也将更大，看来是不可行的，呵呵。另外，我还有一点不成熟的想法。
       我想既然ELBE既有天然的“smooth”流场的功能，可不可以将其扩展到可压缩领域，因为在可压缩领域，捕捉激波正好需要这种功能，当然还是需要对这种“smooth”功能要有比较深入的理解，才能用的恰到好处，使其仅仅激波位置起作用，而其他位置不起作用，不至于污染其他地方的解 ？ 但是我又觉得可能会有问题，因为ELBE是基于熵信号来判断的，在熵层中可能会起作用。
       一点胡乱猜想，呵呵。希望大家给予点拔。

[ 本帖最后由 lwd1981 于 2012-10-17 23:59 编辑 ]

luo@odu.edu

I do not think your proposal will work for the following reason. As I have pointed out in my Reply to KSC, there is NO thermodynamics in the "ELBE" -- the "entropy" in the ELBE model is a stabiliser or a Lyapunov function. In other words, this so-called "entropy" (and the temperature as well) in the ELBE model does NOT satisfy the thermodynamic equation the usual entropy satisfies.

BTW, this idea has been tested and failed (see the work by Packwood which cited in my Reply).

The bottom line -- there is no magic.

lwd1981

非常感谢罗老师的回复。我再仔细研读一些您的文章，呵呵