Fix algorithm of IdealGases.Common.Functions.s0_Tlow_der

[beutlich]

@finback-at @thorade FYI

Fix #2870, fix #1909.

[finback-at]

I checked that the code is same as cp_Tlow(data,T)/T and it's all right.
That you!

[finback-at]

Sorry, I dropped T_der in my comment. The code value is same as,

T_der * cp_T_low(data,T)/T,

and It's OK!

[tobolar]

...I dropped T_der in my comment...

In that case you can simply edit your comment again:

[thorade]

My understanding of #1909 was that the smoothOrder annotation is preferred!?
So the better solution would be to use smoothOrder here, and also for cp_T.
The derivative functions still cannot be deleted, because they are called explicitly from MoistAir.

[beutlich]

Well, stating the derivative was easier for me (as I do not know which smooth order to set).

[casella]

My understanding of #1909 was that the smoothOrder annotation is preferred!?
So the better solution would be to use smoothOrder here, and also for cp_T.

I agree with @thorade. For functions which are not too involved, I think it is preferrable to leave the tools compute the derivatives via AD. This is certainly the case for these functions, which are based on generalized polynomials, logarithms, and other expressions for which derivative are computed in the most straightforward way by AD.

This makes the codebase smaller and more reliable, and avoids potential errors. AFAIK also OpenModelica supports this option.

[casella]

Well, stating the derivative was easier for me (as I do not know which smooth order to set).

The original functions are analytic, so they can be differentiated as many times as one wants. In practice, thermodynamic systems are at most index 1, so I guess you can write smoothOrder = 2 and that will be more than enough for all practical applications.

[casella]

I would suggest to add the smoothOrder=2 annotation as explained in my comment.

[beutlich]

I would suggest to add the smoothOrder=2 annotation as explained in my comment.

OK. Resolved.

[beutlich]

@hubertus65 @wischhusen @casella Please add your review.

[beutlich]

@thorade OK for you to merge?

[thorade]

Yes, good to merge, IIRC this was the version that passed the test.