On the positivity of an auxiliary function of the BGK model for slow chemical reactions. (English) Zbl 1457.80012
Summary: We show that an auxiliary function of the BGK model for slow chemical reactions that corresponds to the local temperature in the case of the original BGK model for inert gases, can take negative values.
MSC:
| 80A32 | Chemically reacting flows |
| 76N15 | Gas dynamics (general theory) |
| 92E20 | Classical flows, reactions, etc. in chemistry |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
References:
| [1] | Groppi, M.; Spiga, G., A bhatnagar—Gross—Krook-type approach for chemically reacting gas mixtures, Phys. Fluids, 16, 12, 4273-4284 (2004) · Zbl 1187.76189 |
| [2] | Monaco, R.; Pandolfi Bianchi, M., A BGK-type model for a gas mixture with reversible reactions, (New Trends in Mathematical Physics (2004), World Sci. Publ.: World Sci. Publ. Hackensack, NJ), 107-120 · Zbl 1088.76073 |
| [3] | Rossani, A.; Spiga, G., A note on the kinetic theory of chemically reacting gases, Physica A, 272, 563-573 (1999) |
| [4] | Andries, P.; Aoki, K.; Perthame, B., A consistent BGK-type model for gas mixtures, J. Stat. Phys., 106, 993 (2002) · Zbl 1001.82093 |
| [5] | Groppi, M.; Rjasanow, S.; Spiga, G., A kinetic relaxation approach to fast reactive mixtures: Shock wave structure, J. Stat. Mech. Theory. Exp., P10010 (2009) |
| [6] | Brull, S.; Schneider, J., Derivation of a BGK model for reacting gas mixtures, Commun. Math. Sci., 12, 7, 1199-1223 (2014) · Zbl 1311.35176 |
| [7] | Bisi, M.; Spiga, G., On kinetic models for polyatomic gases and their hydrodynamic limits, Ric. Mat., 66, 1, 113-124 (2017) · Zbl 1373.76292 |
| [8] | Bisi, M.; Spiga, G., On a kinetic BGK model for slow chemical reactions, Kinet. Relat. Models, 4, 1, 153-167 (2011) · Zbl 1218.80018 |
| [9] | Groppi, M.; Spiga, G., A kinetic relaxation model for bimolecular chemical reactions, Bull. Inst. Math. Acad. Sin. (N.S.), 2, 2, 609-635 (2007) · Zbl 1132.82014 |
| [10] | Bisi, M.; Conforto, F.; Monaco, R.; Ricciardello, A., On the steady deflagration process for a gas mixture undergoing irreversible reactions, Ric. Mat., 68, 1, 13-35 (2019) · Zbl 1415.76744 |
| [11] | D. Kim, M.-S. Lee, S.-B. Yun, Stationary BGK models for chemically reacting gas in a slab, Submitted. Available at https://arxiv.org/abs/2002.06464. |
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