LBM的CFL条件

lwd1981

谢谢罗老师的回复，呵呵。

onesupeng

原帖由 luo@odu.edu 于 2012-9-6 00:03 发表

                               
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There are indeed many publications, especially those written by experts from Exa Corp., which claim explicitly and unambiguously that one of the important advantages of the LBE is that CFL = dx/dt =1, ...

谢谢罗老师的讲解。我主要是不认同这种定义和说法。当然把dx=dt=1的定义方式，由于是整数操作，可能会节省一定的内存和计算，但非要把这个和CFL联系在一起，说CFL=1，总觉得怪怪的。

lwd1981

“波速是流体流速+音速，也是对流项的雅克比多项式的特征值”，这句话只对了一半，对流项的雅克比多项式的特征值是波速是对的，但是波速是流体流速+音速是不对的，流体流速+音速是NS方程的动量方程的波速，不是所有波动方程的波速都非要加个声速，这也是某篇有关非结构有限体积LBM发在JCP上漏洞百出的论文里面的错误.

zqb138

怎么就都纠结到标准LBM上了呢？

我的提问显然是非结构网格，不是那个直角网格；方程也不是标准形式，而是微分形式。
有这么大的区别，数值方法大不相同的。

我现在只想知道对微分形式做数值模拟，那个e怎么给？dt怎么给？

zqb138

亲们，不要跑题！

wdlxmzd

Usually, the CFL number is defined as =u*dt/dx (1d). u is the character velocity. in standard lb, if you define u=c, then CFL=1.

wdlxmzd

for non-standard lb,  you can take a look at some references about finite difference LB, such as the paper: JCP, 143 V, Pages 426-. you can also set c=1, then determine dt via CFL condition. c*dt/dx, here dx is the smallest dx in the computational domain.

wdlxmzd

c=dx/dt is used to derive standard lb, there is no such a relation in non-standard. you can choose a value for c, then determine dt. Also, if you have time, you can examine the effects of c by investigating different values of c.

lwd1981

In fact, I have already  answer that.
In one time step,the CFL number equals one when the flow field information is transferred  one grid precisely along the characteristic direction, which fits for any  wave type equation.

lwd1981

在标准LBM中时间步长和空间步长是关联的，但在LBE中这个要求被放弃了，所以我前面讲过，C=dx/dt 可以任意取，但是要满足小M和小Kn的前提。在LBE中C的定义仅仅是为了定义格子“声速”，因为格子“声速”Cs=C/sqrt(3).

onesupeng

原帖由 zqb138 于 2012-9-6 08:21 发表

                               
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怎么就都纠结到标准LBM上了呢？

我的提问显然是非结构网格，不是那个直角网格；方程也不是标准形式，而是微分形式。
有这么大的区别，数值方法大不相同的。

我现在只想知道对微分形式做数值模拟，那个e怎么 ...

这个你要请下面帖子的楼主帮忙，因为他已经会了
http://cfluid.com/bbs/viewthread.php?tid=116111&extra=page%3D1

luo@odu.edu

If you "define u=c", you are not doing CFD, to say the least -- for this "definition" does not confirm the original meaning and significance of the CFL number.

wdlxmzd

in my opinion, the CFL number is no use in standard lb. In non-standard, the cfl number may be used to choose dt. However, there are seemingly no theories that show how to choose the cfl number. choose 0.5? or 0.05?  Therefore the CFL number in the lb method cannot provide its service in the conventional methods. in non-standard lb It is used to choose dt empirically.

hence it makes no  sense to debate its definition. Several experts claimed that u=|u|_max/C_s, and then cfl = Ma_max. Can we use this definition to determine dt? Obviously can't, since we don't know which value of cfl number will give stable solution.

btw. i hope to learn from Prof. Luo about the relaxation times of MRT. there have been some guidences about how to choose different times, but it is seemingly still enough. In your paper, there are MRT, MRT 1, MRT 2, 3, .... You have shown that sometimes, MRT is better than another one, but in somes cases, it is inferior. Is there any theory or explanation about this problem?

lwd1981

"However, there are seemingly no theories that show how to choose the cfl number. choose 0.5? or 0.05?  Therefore the CFL number in the lb method cannot provide its service in the conventional methods. in non-standard lb It is used to choose dt empirically. "

I am afraid that I can not accept that. In my opinion, Since LBE are also PDEs, they should satisfy the numerical stability conditions of PDE  when they solved by numerical methods. For LBE, the most important constrain comes from the stiff collision item, which is more severe than  the Courant-Friedrick-Lewy condition from
convection stability. Of course, for explicit method, the CFL number seems no meaning, but if you use implicit collision item, the time step will be limited by Courant-Friedrick-Lewy condition, from which you can get the maximum CFL number.

onesupeng

楼上还是用汉语吧，最后那句说反了吧

另外，一帮人在谈CFL，CFL是什么啊，有没有人能讲清楚？