Reconsider composition state variables for reactors, flames, and other systems

[ischoegl]

Creating feature request from #91. Going through a major release opens the opportunity for a breaking change.

Discussed in #91

^{Originally posted by speth February 9, 2021}
Motivation

Cantera's governing equations for reactors and flames currently use mass fractions as the state variables for the composition. This approach leads to fairly simple equations for the most common cases, but introduces some thorny mathematical issues due to the constraint that the sum of the mass fractions should be 1 that make it difficult to solve certain problems. While we have workarounds in place for some of these issues, these workarounds are often fragile. Some specific examples:

• Calculating reasonable Jacobians requires leaving the sum(Y) = 1 constraint unsatisfied. In this case, there is no fully consistent way to calculate mole fractions, or any quantities which are computed from mole fractions. This is a concern for computing mixture averaged transport fluxes, proportional to the mole fraction gradients, and for any non-ideal thermo model where properties are calculated based on mole fractions.

• Without the sum(Y) = 1 constraint, steady-state solvers are difficult to use because (depending on the situation), they can find the "solution" of setting all mass fractions to zero. This is particularly a problem for steady-state surface coverage problems.

Possible Solutions

These issues could be resolved by using concentrations or species masses as the species state variables instead.

References

Cantera/cantera#390