Adding small CSTRs slow down simulation

[schmoelder]

To simplify the setup of large multi-column systems, the CarouselBuilder in CADET-Process adds small CSTR units for each zone inlet and outlet which serve to distribute the in- and outgoing streams. However, we noted that this massively slows down the simulation time compared to a setup without these distributor valves. For example, using a standard 4-Zone SMB without the CSTRs, the simulation time is ~10 s for 10 cycles. Adding the CSTRs increases this to ~40 s.

Trying to figure out what causes the slow-down, @ronald-jaepel suggested replacing the CSTRs with a LRM(P) with the same (small) volume and a single cell (using FV). This actually reduced simulation time down to ~20 s, which is still a bit more than I had hoped for but it is a large improvement. So something seems "off" with the CSTR.

Our first hypothesis was that even though in this case Q_in == Q_out for all CSTRs, the volume is still updated for each time step. Small variation due to floating point precision, combined with the fact that volumes in SI units are always awkwardly small, could make the system very stiff, increasing the simulation time.

@jbreue16 created an alternative CSTR unit operation with constant volume (see https://github.com/modsim/CADET/tree/feature/cstr_const_volume). However, first tests did not improve the simulation times at all (still ~40 s). So the hunt continues...

[lieres]

Puh, I was hoping for something else. Have you set the dispersion coefficient $D=0$ in the LRM(P) tests?

[AntoniaBerger]

When simulating a CSTR (system), the calculation time apparently depends on its volume and the ratio to the concentration fed into the sections.
The concrete observation so far is:
If the injected concentration is greater than the volume of the CSTR, the simulation of the CSTR (system) is up to ~4.5x slower than if the injected volume is less than or equal to the volume. For example, in a system with 5 CSTRs with a volume of 1E-3 each, a sudden increase in simulation time can be observed as soon as a concentration of more than 1E-3 is injected. (calculation script).

Furthermore, we investigated which parts of Cadet contribute to the overall runtime. An overview of the findings is shown below. Each case involves 5 CSTRs, a cycle time of 500 minutes, 10 cycles, and adjusted relative and absolute tolerances.

[AntoniaBerger]

For a more structured analysis, the table below compares the exact calculation times for CADET-Core, CADET Python and CADET - Process for a CSTR and LRM system.

A more detailed profile analysis indicates that the overhead of the 4th case (CSTR with volume 1E-4 and injected volume 1E-3) is largely addessable to writing the results in the h5 file (see figure below). This also align with the observation that adjusting the tolerances for the integrater had no effect on the runtime behavior from the table abouve.

It would be interesting to see whether this problem also occurs with the new C-API.