mean, variance and covariance statistics of any field function on any part.
StarCCM+ documentation says this from version 2.06.004 :
" A new ability to compute the mean, variance and covariance statistics of any field function on any part. The primary driver for this is LES and DES where you might want to compute means or stresses from the instantaneous velocity, or the mean skin friction or heat transfer on a wall. " How does one do this? via monitor or via new field function. If I do a new field function, say for Velocity: XComponent, what should the variance definition be? I saw one example where it said $MixtureFractionVariance so I tried this as a new field function $Velocity_0Variance BUT I am getting syntax error in the assembly code. Can anyone tell me the definition of variance for U velocity and mean of U velocity? Thanks! 
Right click on Monitors > New Monitor ...

okay I have done that in the past BUT it remains as a monitor.
What about if I want that monitor variable to be written out in a Table for every time step for a specific part in the computational domain? Are you saying once I create that Monitor variable it then shows up as a Variable in the field functions too? 
Doesn't look like it shows up as a Field Function. But, you can easily export a table by rightclicking and selecting "Export." In the definition of a monitor, you can specify whether to tabulate versus iteration or time step.

The problem I am having when I am using the Field Function Monitor is this:
Successfully able to create the field variance monitor BUT for the part choice it is only allowing me to select parts from the entire computational domain and the boundary parts BUT not a selective Derived Part I have in the tree. If I look up documentation under "What is a Field Function Monitor?" I see the documentation as " Once you set their Field Function and Parts properties, these monitors can be displayed as scalar quantities just like other field functions. " This is where I am failing to select my desired Derived Part and Tabulate the results. What am I missing? 
I can confirm that you can't select Derived Parts as input for these Field Monitors in v4.06
In terms of using it as a scalar, when I create a Mean Monitor of Pressure Coefficient on some part, in its definition, under Title, the name of the corresponding Field Function is given. In this case, it's "Mean of Pressure Coefficient." If you only care about an average of some quantity on a derived part for the current time step, you can always create an Area Averaged report and plot that. 
My goal is slightly different.
I want to establish Turbulent Statistics for Unsteady simulations in DES and LES. If these mean, variance were working correctly then the simulation itself would be keeping track of the time averaging and I could then export out the tabulated results once turbulence statistics long term (time > Infinity) has been established. So for example I want to get Re UU stress = (1/N)Sum((U(i)  UMean), {i,1,N}) and N is a very large number, say 10000 Right now I am constrained to writing Macro to get the primary variables and write them out and do the post processing outside StarCCM+ that is very time consuming. When I read the portion in the documentation that mean, variance, covariance of any part can be calculated for any part in an unsteady simulation I wanted to know if someone had used it since I was having a hard time to get it to work. 
small correction on my UU stress definition
Re UU stress = (1/N)Sum((U(i)  UMean)^2, {i,1,N}) and N is a very large number, say 10000 
Yeah, too bad you can't specify Derived Parts as inputs to these monitors. I'll put in a feature request, so it might get implemented, in a year or so ..., in the meantime I'll think about it some more, good luck!

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