{"title":"Regression Models for Calculating State-to-State Coefficients of the Rate of Vibrational Energy Exchanges","authors":"A. A. Isakov, V. I. Gorikhovskii, M. Yu. Melnik","doi":"10.1134/s1063454124700079","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper proposes an effective algorithm for solving problems of nonequilibrium gas dynamics taking into account detailed state-to-state vibrational kinetics. One of the problems of traditional methods is their high computational complexity, which requires a lot of time and memory. The work explored the possibilities of using relaxation rate prediction to improve the performance of numerical simulations of nonequilibrium oxygen flows instead of direct calculations. For this purpose, an approach based on a nonlinear regression analysis was used, which made it possible to obtain computationally efficient approximation formulas for the energy exchange rate coefficients in the model of a Forced Harmonic Oscillator, taking into account free rotations (FHO-FR), to significantly increase the calculation speed while maintaining accuracy, and to construct an optimized model FHO-FR-reg. Using the obtained regression formulas, numerical modeling was carried out, which made it possible to validate the model for the problem of oxygen flow behind an incident and reflected shock wave. A comparison between the Forced Harmonic Oscillator (FHO) and the FHO-FR models is not possible due to the high computational complexity of the second model. With the advent of a common approximation model, it became possible to compare simulation results for these models. Numerical calculations have shown that the FHO-FR–reg model gives values of gas-dynamic parameters close to the FHO model. The developed regression models make it possible to speed up the solution to the problem of modeling oxygen relaxation several times compared to other models of similar accuracy.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454124700079","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper proposes an effective algorithm for solving problems of nonequilibrium gas dynamics taking into account detailed state-to-state vibrational kinetics. One of the problems of traditional methods is their high computational complexity, which requires a lot of time and memory. The work explored the possibilities of using relaxation rate prediction to improve the performance of numerical simulations of nonequilibrium oxygen flows instead of direct calculations. For this purpose, an approach based on a nonlinear regression analysis was used, which made it possible to obtain computationally efficient approximation formulas for the energy exchange rate coefficients in the model of a Forced Harmonic Oscillator, taking into account free rotations (FHO-FR), to significantly increase the calculation speed while maintaining accuracy, and to construct an optimized model FHO-FR-reg. Using the obtained regression formulas, numerical modeling was carried out, which made it possible to validate the model for the problem of oxygen flow behind an incident and reflected shock wave. A comparison between the Forced Harmonic Oscillator (FHO) and the FHO-FR models is not possible due to the high computational complexity of the second model. With the advent of a common approximation model, it became possible to compare simulation results for these models. Numerical calculations have shown that the FHO-FR–reg model gives values of gas-dynamic parameters close to the FHO model. The developed regression models make it possible to speed up the solution to the problem of modeling oxygen relaxation several times compared to other models of similar accuracy.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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