Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)4525610.22363/2658-4670-2025-33-2-184-198BPOFHSModeling and SimulationМатематическое моделированиеResearch ArticleInterval models of nonequilibrium physicochemical processesИнтервальные модели неравновесных физико-химических процессовhttps://orcid.org/0000-0003-0364-866557203389215ABC-7836-2021MorozovAlexander Yu.МорозовА. Ю.

Doctor of Physical and Mathematical Sciences, Senior Researcher, Department of Mathematical Modeling of Heterogeneous Systems, Federal Research Center Computer Science and Control of the Russian Academy of Sciences; Associate Professor of the Department of Computational Mathematics and Programming, Moscow Aviation Insti- tute (National Research University)

morozov@infway.ruhttps://orcid.org/0000-0003-0998-79756602701797T-4571-2018ReviznikovDmitry L.РевизниковД. Л.

Doctor of Physical and Mathematical Sciences, Professor, Leading Researcher, Department of Math- ematical Modeling of Heterogeneous Systems, Federal Research Center Computer Science and Control of the Russian Academy of Sciences; Professor of the Department of Computational Mathematics and Programming, Moscow Aviation Institute (National Research University)

reviznikov@mai.ruhttps://orcid.org/0000-0002-5119-44886506396733B-4572-2019GidaspovVladimir Yu.ГидасповВ. Ю.

Doctor of Physical and Mathematical Sciences, Associate Professor, Professor of the Department of Computational Mathematics and Programming

gidaspov@mai.ruFederal Research Center Computer Science and Control of the Russian Academy of SciencesФедеральный исследовательский центр “Информатика и управление” Российской академии наукMoscow Aviation Institute (National Research University)Московский авиационный институт (национальный исследовательский университет)15072025332VOL 33, NO2 (2025)ТОМ 33, №2 (2025)18419825072025Copyright ©; 2025, Morozov A.Y., Reviznikov D.L., Gidaspov V.Y.Copyright ©; 2025, Морозов А.Ю., Ревизников Д.Л., Гидаспов В.Ю.2025Morozov A.Y., Reviznikov D.L., Gidaspov V.Y.Морозов А.Ю., Ревизников Д.Л., Гидаспов В.Ю.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/45256

The paper discusses the application of the adaptive interpolation algorithm to problems of chemical kinetics and gas dynamics with interval uncertainties in reaction rate constants. The values of the functions describing the reaction rate may differ considerably if they have been obtained by different researchers. The difference may reach tens or hundreds of times. Interval uncertainties are proposed to account for these differences in models. Such problems with interval parameters are solved using the previously developed adaptive interpolation algorithm. On the example of modelling the combustion of a hydrogen-oxygen mixture, the effect of uncertainties on the reaction process is demonstrated. One-dimensional nonequilibrium flow in a rocket engine nozzle with different nozzle shapes, including a nozzle with two constrictions, in which a standing detonation wave can arise, is simulated. A numerical study of the effect of uncertainties on the structure of the detonation wave, as well as on steadyystate flow parameters, such as the ignition delay time and the concentration of harmful substances at the nozzle exit, is performed.

В данной работе рассматривается применение алгоритма адаптивной инетрполяции к задачам химической кинетики и газовой динамики с интервальными неопределенностями констант скоростей реакций. Значения функций, описывающих скорость реакции, могут значительно различаться, если они были получены разными исследователями. Разница может достигать десятков или сотен раз. Для учета данных различий в моделях предлагается использовать интервальные неопределенности. Решение таких задач с интервальными параметрами выполняется с помощью ранее разработанного алгоритма адаптивной интерполяции. На примере моделирования горения смеси водорода и кислорода демонтируется влияние неопределенностей на процесс протекания реакций. Моделируется одномерное неравновесное течение в сопле ракетного двигателя с разной формой сопла, включая сопло с двумя сужениями, в котором может возникать стоячая детонационная волна. Выполняется численное исследование влияния неопределенностей на структуру детонационной волны, а так же на параметры установившегося течения, такие как время задержки воспламенения и концентрация вредных веществ на выходе из сопла.

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