Numerical design rationale

This page records numerical choices visible in audited Arrhenius.jl and Cantera source paths, the reasons available in source history, and tests identified by the audits. It is a source comparison, not a claim that the solvers produce identical solutions.

Scope. Arrhenius.jl refers to audited source snapshot 78ab438, flame mode discretization=:finite_difference, except where point APIs/reactors are named. Cantera refers to 4.0 development source at commit 726522be4e2a13454d8415b7ef799d621f665cf3, with mixture-averaged transport and no Soret/radiation by default. Cross-code survey: 2026-10-16. “Identical” means same rule/constants in the audited mode, not bitwise equality; “different” describes implementation, not merit. All comparison code references below are public.

Many original Cantera constants predate surviving issue/PR records. Where motivation cannot be established, it is stated as unknown rather than inferred. Cantera's original 1-D solver cites Kee, Coltrin, and Glarborg’s Chemically Reacting Flow (publisher record). Cantera line links are pinned to the source SHA. Tests are those identified in the audits; “none found” means no dedicated test was located.

1. Unknowns and scaling

2. Discretization

3. Property updates and Jacobian

4. Newton: norms, bounds, damping, convergence

5. Time stepping

6. Refinement and domain

7. Trace and negative species

8. Kinetics, thermo, and transport point evaluation

9. Reactors

References

Publication records below are linked to DOI/publisher records and transcribed from DOI metadata. Code and PR links above evidence implementation; these papers provide algorithm lineage or software context.

• Grcar et al. 1988, publisher DOI.
• Cuoci et al. 2015, publisher DOI.
• Long et al. 2018, publisher DOI.
• Lapointe et al. 2019, publisher DOI.
• Kee, Coltrin, Glarborg 2003, Wiley record.

@article{Grcar1988,
 author={Grcar, Joseph F. and Kee, Robert J. and Smooke, Mitchell D. and Miller, James A.},
 title={A hybrid {Newton}/time-integration procedure for the solution of steady, laminar, one-dimensional, premixed flames},
 journal={Symposium (International) on Combustion}, publisher={Elsevier BV}, year={1988},
 volume={21}, number={1}, pages={1773--1782}, doi={10.1016/S0082-0784(88)80411-9},
 url={https://doi.org/10.1016/S0082-0784%2888%2980411-9}
}
@article{Cuoci2015,
 author={Cuoci, A. and Frassoldati, A. and Faravelli, T. and Ranzi, E.},
 title={{OpenSMOKE++}: An object-oriented framework for the numerical modeling of reactive systems with detailed kinetic mechanisms},
 journal={Computer Physics Communications}, publisher={Elsevier BV}, year={2015}, volume={192}, pages={237--264},
 doi={10.1016/j.cpc.2015.02.014}, url={https://doi.org/10.1016/j.cpc.2015.02.014}
}
@article{Long2018,
 author={Long, Alan E. and Speth, Raymond L. and Green, William H.},
 title={Ember: An open-source, transient solver for {1D} reacting flow using large kinetic models, applied to strained extinction},
 journal={Combustion and Flame}, publisher={Elsevier BV}, year={2018}, volume={195}, pages={105--116},
 doi={10.1016/j.combustflame.2018.05.001}, url={https://doi.org/10.1016/j.combustflame.2018.05.001}
}
@article{Lapointe2019,
 author={Lapointe, Simon and Whitesides, Russell A. and McNenly, Matthew J.},
 title={Sparse, iterative simulation methods for one-dimensional laminar flames},
 journal={Combustion and Flame}, publisher={Elsevier BV}, year={2019}, volume={204}, pages={23--32},
 doi={10.1016/j.combustflame.2019.02.030}, url={https://doi.org/10.1016/j.combustflame.2019.02.030}
}
@book{Kee2003,
 author={Kee, Robert J. and Coltrin, Michael E. and Glarborg, Peter},
 title={Chemically Reacting Flow: Theory and Practice}, publisher={Wiley}, year={2003},
 isbn={9780471461296}, doi={10.1002/0471461296}, url={https://doi.org/10.1002/0471461296}
}