In the context description of this use case, the Unit Manager is given a job that is not described before (especially when the Unit Manager is listed as an Actor): the Unit Manager is supposed to set the time step on each Flowsheet Unit.

My understanding of the Unit Manager, at least in the context if steady-state simulation, is that it was not involved in the actual simulation. It was there to act at the stage where the flowsheet is built. The Flowsheet Solver is there to resolve the system. So I would propose to change the actor in that Use Case to Flowsheet Solver.

Agreed

I agree that the sentence is difficult to understand. This is to show that all unit operations stay in their current time step until the flowsheet solver accepts the results and performs calls to accept the time step.
so the sentece could be:

"The <Flowsheet> stays in current time step until the <Flowsheet> has accepted the time step."

In this case the Actor <Flowsheet> would need to be defined in 2.2.1

Is the Flowsheet really a possible Actor? Is the Flowsheet performing any action? On the other hand the "Flowsheet Solver" seems to be an actor. It performs the resolution of the equations describing the connections between the UOs in the Flowsheet.

I agree, how about:

"The flowsheet stays in current time step until the <Flowsheet> has accepted the time step."

What is behind the Flowsheet? If one says that it accepts the time step, it is indeed an actor. But I can't see the whole Flowsheet as an actor. My understanding is that the Flowsheet Solver will reach a point where it knows that the time step has converged. So It would rather say the each UO in a Flowsheet stays at the current time step till the Flowsheet Solver says otherwise. Not well phrased but it is the idea I would like to pass.

It was meant to say:

"The flowsheet stays in current time step until the <Flowsheet> has accepted the time step."

Hmm, the web site is playing tricks on me. Trying again:

"The flowsheet stays in current time step until the <Flowsheet> has accepted the time step."

Ok - that obviously does not work. Replacing the angled brackets by square ones:

"The flowsheet stays in current time step until the [Flowsheet Solver] has accepted the time step."