Abstract

Numerical modeling of nonequilibrium state-to-state carbon dioxide kinetics is a challenging time-consuming computational task that involves solving a huge system of stiff differential equations and requires optimized methods to solve it. In the present study, we propose and analyse optimizations for the Extended Backward Differential Formula (EBDF) scheme. Using adaptive timesteps instead of fixed ones reduces the number of steps in the algorithm many thousands of times, although with an increase in step complexity. The use of parallel computations to calculate relaxation terms allows one to further reduce the computation time. Numerical experiments on the modeling of spatially homogeneous carbon dioxide vibrational relaxation were performed for optimized computational schemes of different orders. Based on them, the most optimal algorithm of calculations was recommended: a parallel EBDF scheme of fourth-order with an adaptive timestep. This method takes less computational time and memory costs and has the high stability.

中文翻译：

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全状态法优化CO 2振动动力学模型

摘要

非平衡状态到状态二氧化碳动力学的数值模拟是一项艰巨的耗时计算任务，涉及求解庞大的刚性微分方程组，并且需要优化的方法来求解。在本研究中，我们提出并分析了扩展后向微分公式（EBDF）方案的优化。使用自适应时间步长而不是固定时间步长可减少算法中的步长数以千计，尽管步长复杂度会增加。使用并行计算来计算弛豫项可以进一步减少计算时间。针对不同阶次的优化计算方案，进行了空间均质二氧化碳振动弛豫建模的数值实验。基于它们，推荐了最佳的计算算法：具有自适应时间步长的四阶并行EBDF方案。该方法占用较少的计算时间和存储成本，并且具有很高的稳定性。