[HLo]

Hello Atze,
I did some experiments as well, comparison of integration with: A) an additional variable and B) with a fortran function in both transient and steady state runs. The fortran routine implements trapezoidal rule and takes account of timestep length.

transient, constant and varying timestep lenghts:
both solutions do their work but with "slightly" different results
A) the very first integrated value of a quantity q is calculated as: q0 + q*dt1 (q0 is initial value dt1 is 1st timestep length)
B) the fortran implemetation uses trapezoidal rule so gives 1/2*(q+q0)*dt1
-this main deviation is kept the entire simulation if one doesn't supply a "dummy" initial value q0
-minor deviations appear but these may be explained this way:
fortran gives 1 output value for 1 input quantity, whereas the AV solution uses a volume integral or mean value over a output quantity with spatial and/or numerical "noise" inside

steady state:
-the deviations found in transient are the same
-the result gives a reasonable integration value, if physical timesteps are chosen
- On automatic timesteps a "false timestep" is used, but there is no way to access it from fortran, so I expect the compensated (see conclusion) AV solution to be of advantage, not beeing sure how the intgrated value has to be interpreted, when no "real" time value is given

conclusion:
If one consideres to post process the integrated quantity in CFX-Post an AV ist needed anyway, one might prefer the AV solution, with an initial value which is minus one half of the expected quantity times 1st timestep: -0.5*q*dt1.
Unfortunately the initial value cannot be expressions, so a value has to be calculated in advance.
Both solutions give good results in transient runs, steady state runs need further investigations and considerations how the results have to be interpreted