Solver divergence with large quadratic resistances.

Description

When a 0D system features large stenosis (quadratic) resistances, especially if they vary in sign. The solver often diverges, that is, the linear Newton solver in the time-stepping scheme is not able to sufficiently reduce the residual. This is somewhat expected, because the introduction of large quadratic resistances of varying sign means the relationship between the solution variables and the residual is not monotonic or convex. There is technically no guarantee that a solution exists.

Reproduction

bifurcations_EL_NN_JunctionOnly.json

Sample input files with large quadratic resistances that diverges.

Expected behavior

Ideally, the solver should converge if there is a solution, and print an error if not.

Additional context

No response

Code of Conduct

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Start with bifurcations_EL_NN_JunctionOnly.json to reproduce divergence in the 0D system. Trace the time-stepping scheme's linear Newton solver and how it handles large, sign-varying quadratic resistances. Done means convergent cases converge when a solution exists, while cases without a solution report an error.