Calculating Volumetric Flow Rate at Internal Boundary

There is even more to this, as you need to add the MeshFunction for cells to this, as explained in Integrating over an interior surface - #4 by MiroK

In DOLFINx, one can reduce it to a one-sided internal integral, as explained in for instance: Add one-sided integration example as example of custom integration · Issue #158 · jorgensd/dolfinx-tutorial · GitHub or use the same notion of custom integration to consistently orient the integration entities of a dS integral.