Counterflow solution strategy

[g3bk47]

Currently, an "extinct flame" solution is treated as successful solution for counterflow flames. Therefore, trying to find a solution by first disabling the energy equation is never tried. However, this can significantly increase the chance of finding the non-extinct solution. This PR modifies the solution strategy for counterflow flames so that after an extinct flame solution is found, the normal workflow of trying another solution with disabled energy equation is applied. Previous discussion can be found in Cantera/enhancements#155.

Checklist

• The pull request includes a clear description of this code change
• Commit messages have short titles and reference relevant issues
• Build passes (scons build & scons test) and unit tests address code coverage
• Style & formatting of contributed code follows contributing guidelines
• The pull request is ready for review

[codecov]

Codecov Report

Merging #1463 (aac4bf1) into main (8b5a0e9) will increase coverage by 0.03%.
The diff coverage is 100.00%.

❗ Current head aac4bf1 differs from pull request most recent head a570f71. Consider uploading reports for the commit a570f71 to get more accurate results

@@            Coverage Diff             @@
##             main    #1463      +/-   ##
==========================================
+ Coverage   69.86%   69.90%   +0.03%     
==========================================
  Files         377      377              
  Lines       57298    57301       +3     
  Branches    19164    19164              
==========================================
+ Hits        40033    40054      +21     
+ Misses      14712    14694      -18     
  Partials     2553     2553              

Impacted Files	Coverage Δ
interfaces/cython/cantera/_onedim.pyx	81.05% <100.00%> (+1.70%)	⬆️

... and 1 file with indirect coverage changes

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[ischoegl]

@g3bk47 … thank you for the PR! Apart from squashing the ‘fixing line length’ commit, could you comment on the odd dip in temperature for U=7 m/s in your original post Cantera/enhancements#155 (comment)? I’m a little concerned as is looks like an artifact that we’d like to avoid. I realize that you pointed this out yourself …

[g3bk47]

Hi @ischoegl,
I merged the two commits and took a closer look at the example from Cantera/enhancements#155:
The cause for the odd dip (black dashed line below) was that I set the tolerances to very high values in my test script so that some of the flame "solutions" contained only a hand full of points. After changing
f.set_refine_criteria(ratio=4, slope=0.2, curve=0.3, prune=0.04)
to
f.set_refine_criteria(ratio=2.5, slope=0.05, curve=0.05, prune=0.005)
I get pretty much perfect agreement between the direct solution using the new code (blue solid line) and the continuation method (red dotted line) in terms of maximum temperature:

[ischoegl]

Thanks, @g3bk47 ... this looks good to me, and the explanation makes sense. Regarding the CI failures, they are unrelated - see #1471.