[WIP] Implementing variable density for unsteady incompressible flow

[tkiymaz]

Proposed Changes

Implements variable density treatment for unsteady incompressible flow simulations. Currently, SU2 uses constant density in transient simulations, which is inaccurate for combustion cases where density varies significantly due to heat release and species composition changes. This contribution enables proper density updates during time-stepping for flamelet-based combustion modeling. For now, only 1st order time marching is implemented

Related Work

Related to incompressible flow solver and flamelet combustion modeling. No specific issue linked yet.

PR Checklist

• [X] I am submitting my contribution to the develop branch.
• [X] My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• [X] My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• [ ] I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• [ ] I have added a test case that demonstrates my contribution, if necessary.
• [ ] I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

[pcarruscag]

@Cristopher-Morales can you review this pr please?

[Cristopher-Morales]

@Cristopher-Morales can you review this pr please?

Hi @pcarruscag !

Yes, I can help reviewing this PR.

Please let me know if you need something else from my side

[bigfooted]

@Cristopher-Morales I guess the changes to the preconditioner can be removed from this PR since we now have your implementation