Steady state initialization through ModelRunner

[jwboth]

Proposed changes

An extension of the ModelRunner is suggested that enables the implicit definition of initial conditions through a steady state solution that complies with boundary conditions and governing equations. The routine requires a small set of control parameters such as convergence criteria for characterizing when to call a state a steady state, and pseudo time discretization parameters. A tutorial is added to illustrate both the functionality and the rationale behind the intialization routine.

The initialization routine essentially runs a pseudo-time stepping routine. It is therefore expected that the code can actually be substantially shortened after #1682 has been finalized. A TODO note is added to model_runner.py to indicate the foreseen changes.

API and placement of code has not been fully thought through (also in light of the changes of time loops).

NOTE: This PR will be used as basis to extend to initialization of reference states.

What types of changes does this PR introduce to PorePy?
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• Minor change (e.g., dependency bumps, broken links).
• Bugfix (non-breaking change which fixes an issue).
• New feature (non-breaking change which adds functionality).
• Breaking change (fix or feature that would cause existing functionality to not work as expected).
• Testing (contribution related to testing of existing or new functionality).
• Documentation (contribution related to adding, improving, or fixing documentation).
• Maintenance (e.g., improve logic and performance, remove obsolete code).
• Other:

Checklist

Put an x in the boxes that apply or explain briefly why the box is not relevant.

• The documentation is up-to-date.
• Static typing is included in the update.
• This PR does not duplicate existing functionality.
• The update is covered by the test suite (including tests added in the PR).
• If new skipped tests have been introduced in this PR, pytest was run with the --run-skipped flag.

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IvarStefansson commented on 2026-07-06T08:35:38Z
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Some of the code is obsolete after recent PRs. I think most of the remaining code should be split between an example and applications.

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IvarStefansson commented on 2026-07-06T08:35:40Z
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I don't think we need this and the next few blocks. Can't we explain the problem more precisely without illustrating, then proceed to the solution (implicit initialization)?

[keileg]

For clarity: This PR is in hiatus, to be picked up after summer.