Geodesic
Modeling of wave patterns at the combustion front
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 4, pp. 538-548.

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In experimental studies of the propagation of combustion waves in gaseous media, it was found that, under certain conditions, autowave - spiral or target - patterns appear at the wave front. The purpose of the present study is to propose a mathematical model that can explain this phenomenon based on the known chemical kinetics of hydrogen combustion. Model. The original detailed model was first reduced to four equations that adequately describe the propagation of the combustion wave. To explain the structures at the combustion front, the model was further reduced to two equations. Results. An analytical study of the resulting model was carried out, which demonstrated that it can describe the occurrence of spiral waves, and the corresponding conditions for the parameters of the model were determined. These analytical results have been confirmed in numerical experiments. Conclusion. Thus, it has been demonstrated that the model constructed on the basis of the reduction of the known kinetic scheme of hydrogen combustion is capable of explaining the experimentally observed autowave patterns at the propagating combustion front.
Keywords: combustion waves, autowave structures, Nonlinear systems, mathematical modeling. 
@article{IVP_2021_29_4_a4,
     author = {E. O. Yakupov and V. V. Gubernov and A. A. Polezhaev},
     title = {Modeling of wave patterns at the combustion front},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {538--548},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2021_29_4_a4/}
}
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E. O. Yakupov; V. V. Gubernov; A. A. Polezhaev. Modeling of wave patterns at the combustion front. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 4, pp. 538-548. http://geodesic.mathdoc.fr/item/IVP_2021_29_4_a4/