Optional valve-state freezing for piecewise valves to prevent Newton cycling with 3D-0D coupling

Problem

The current piecewise valve implementation allows the valve state to flip between 3D newton iterations, leading to Newton cycling and divergence. For GenBC, we fixed this by freezing the valve state at the beginning of each 3D timestep according to the previous timestep's pressure state. While this does lead to occasional pressure/flow spikes at transitions, this is avoidable with a sufficiently small time step and seems to be the simplest solution to the valve cycling problem.

Solution

I have been implementing the feature in this branch. Let me know your thoughts if there would be a better way to solve this problem.

Additional context

No response

Code of Conduct

• I agree to follow this project's Code of Conduct and Contributing Guidelines

Start by comparing the existing piecewise valve implementation with the valve-freezing branch mentioned in the issue, focusing on how valve state is selected across 3D Newton iterations and timesteps. Check the GenBC context and validate that the optional behavior prevents Newton cycling without changing default behavior; done means the feature is integrated and its transition behavior is verified.