Simcenter STAR-CCM+ How to monitor mass imbalance in transient simulations

Monitoring mass balance of a given phase is an important criterion to assess accuracy of a CFD simulation, being it either single phase or multiphase.

In steady state this is trivial to evaluate; you can, for instance, monitor inlet / outlet mass flows in case of an open domain.
When the model is transient computing phase mass balances is more complicated as you need to account for accumulation/depletion of the given phase in the domain.
Applying the continuity equation this would result in:



i.e. the total mass in the domain at t = t1 is equal to the mass at t = 0 s + the total mass that entered the domain in t = [0,t1] - the total mass that left the domain in t = [0,t1].
The difference between the left and right term of this expression is the actual mass balance.
You can easily see that this can be a rather tedious procedure that requires several reports to be set up in Simcenter STAR-CCM+, and you can find this described in a couple of articles linked in the section "Related Articles" for your reference.

You can obtain the same result by using the built-in function "Mass Imbalance" (or "Mass Imbalance of Phase_i" in a multiphase simulation).
This function shows the mass flow imbalance (per-phase) on a cell by cell basis. To calculate the total mass imbalance, follow these steps:

1) Create a Sum Report selecting the needed Mass Imbalance field function, and the whole domain as input Part
2) Create a Monitor from this report
3) Create a Monitor Integral Report and set the Monitor created at point 2 to be the integrand and physical time to be the integration variable. Rename the report to "Total Integrated Mass Imbalance
4) Create a Monitor and Plot from this last report.


Let's compare the results of this procedure with the one highlighted on a simple test case in the article: How to calculate the actual mass imbalance in an unsteady compressible flow simulation? You can see that the results obtained with the described setup are very close to the one obtained in the previous FAQ.
The simulation is saved in Simcenter STAR-CCM+ v2020.1