code_saturne User's Forum

Hello,

I want to know what is "variance" in output when we set "Species transport" in GUI.

When we set "Species transport" in GUI, we can see "scalar" and "variance" in output file and we can visalize it in paraview.
However, although "scalar" means a concentration of something, I don't know what is "variance".

Can someone tell me this?

Best regards,
Tsubasa

Hello,

The variance is related to a scalar's fluctuation. I am not sure of the exact equations, but there should be more info in the theory guide.

Regards,

Yvan

Hello,

Thank you for your reply.

I looked for it in theory guide and then found this, Is this what you mean?
Sorry for trivial question...

Best regards,
Tsubasa

Hello,

Yes, this is the correct section.

Best regards,

Yvan

Hello,

Thank you for your reply.

I understand that "variance" is a kind of fluctuation, but I did not get this infomation in theory guide.

Does "variance" means just variance in sandard statistics like this? Best regards,
Tsubasa

Hello,

What I want to know is
・how is ~a"^2 defined in equation (ii) in the Section 2.3?
・Is is a just variance which is used in standard statistics?

Best regards,
Tsubasa

Hello Yvan and Tsubasa,

Please I also have a question about variance. Following the Time moment related options-Example 1 (https://www.code-saturne.org/cms/sites/ ... eters.html), I calculated the variance of the vector velocity, and got a tensor of 6 components.

In the codes comments, I learned the velocity variance is <UU>-<U><U>. If we define u, v, w as the 3 components for velocity. I checked the results, the XX component of velocity variance is exactly <uu>-<u><u>. But the YY and ZZ components seem not consistent with <vv>-<v><v> and <ww>-<w><w> respectively. Please see the figures below.


So I'm also confused about how the variance is calculated. Also I'm not able to find a detailed description of the function CS_TIME_MOMENT_VARIANCE used in the codes. If some experts can guide me, it will be much appreciated.

Many thanks,
Ruonan

Hello,

These are 2 different notions :

- a variable's variance is a solved variable, sharing a base variable's boundary conditions, and for which an transport equation is solved. There are a few details (not much) in the user or theory documentation, but I am not too familiar with this part of the code. To the best of my knowledge, this is related a a variable's turbulent fluctuations.

- a variance computed as a time moment is simply the variance (in the statistical sense) of a field's values at each selected location in space (usually cell centers). It can be computed using recursive formulas, as described in the article by Pébay you will find in the code's bibliography. Search for the cs_time_moment.c file in the Doxygen documentation for more details.

Best regards,

Yvan

Hi Yvan,

Thanks for your help.

Best regards,
Ruonan