Regression Models for Calculating State-to-State Coefficients of the Rate of Vibrational Energy Exchanges

A. A. Isakov, V. I. Gorikhovskii, M. Yu. Melnik
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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.

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计算振动能量交换速率的态对态系数的回归模型
摘要 本文提出了一种解决非平衡气体动力学问题的有效算法,其中考虑到了详细的状态到状态振动动力学。传统方法的问题之一是计算复杂度高,需要大量时间和内存。这项工作探索了利用弛豫速率预测来代替直接计算提高非平衡氧流数值模拟性能的可能性。为此,采用了一种基于非线性回归分析的方法,从而获得了强制谐波振荡器模型中能量交换率系数的高效计算近似公式,同时考虑了自由旋转(FHO-FR),在保持精度的同时显著提高了计算速度,并构建了一个优化模型 FHO-FR-reg。利用获得的回归公式,进行了数值建模,从而验证了入射和反射冲击波后氧气流动问题的模型。由于强迫谐波振荡器(FHO)模型和 FHO-FR 模型的计算复杂度较高,因此无法进行比较。随着通用近似模型的出现,对这些模型的模拟结果进行比较成为可能。数值计算表明,FHO-FR-Reg 模型给出的气体动力参数值与 FHO 模型接近。与其他精度类似的模型相比,所开发的回归模型可以将氧气弛豫模型问题的解决速度提高数倍。
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来源期刊
CiteScore
0.70
自引率
50.00%
发文量
44
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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Solution of the Local-Boundary-Value Problem of Control for a Nonlinear Stationary System Taking into Account Computer System Verification On the Approximation of the Attraction Field of a Rigid Body by the Attraction Field of Four Material Points of the Same Mass Rigid-Body Dynamics from the Euler Equations to the Attitude Control of Spacecraft in the Works of Scientists from St. Petersburg State University. Part 2 Regression Models for Calculating State-to-State Coefficients of the Rate of Vibrational Energy Exchanges Astronomical Research at the Mathematics Faculty of St. Petersburg University, I
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