[WIP] Preconditioning for multicomponent flows

[Cristopher-Morales]

Proposed Changes

This pull request aims to extend the preconditioning for incompressible multicomponent flows, specifically when FLUID_MIXTURE model is used and energy equation is solved. Changes introduced in this pull request aim to solve directly for the sensible enthalpy instead of temperature. Specifically, the energy equation that is going to be solved for multicomponent flows is given as follows:

and the sensible enthalpy is:

Currently $C_{p}$ does not depend on temperature for FLUID_MIXTURE, but it depends on the mixture composition. So the sensible enthalpy simplifies to $C_{p}*(T-T_{0})$. For problems where $C_{p}$ strongly depends on the temperature, Cantera library will be coupled to SU2. After this pull request is completed, a pull request with a fluid model using Cantera will be done where an energy equation for the total enthalpy will be solved. A PDF document containing further details about this pull request is available at the following link: preconditioning_general_approach.pdf

Related Work

Currently fluid mixture does not work correctly when the energy equation is on, this is mainly due to the fact that the energy equation that must be solved for multicomponent flows is the one mentioned above for the sensible enthalpy and not the energy equation for a perfect gas that is currently solved in SU2.

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.