研究反应BGK模型的动力学和趋于平衡的渐近趋势
Investigating dynamics and asymptotic trend to equilibrium in a reactive BGK model
AI总结：
该研究通过数值模拟分析了反应BGK模型的动力学行为，探讨了混合物趋于热平衡和化学平衡的渐近趋势，验证了虚物种温度等化假设对H-Boltzmann函数单调性的保障作用。
摘要：
我们数值研究了最近一种用于多组分单原子气体混合物的BGK型模型，该模型经历可逆的双分子化学反应。该模型用松弛项代替Boltzmann方程中的碰撞项，从而分别描述机械过程和化学反应的影响。此外，该模型具有自洽性质。当化学贡献中的辅助温度共享共同值时，正确的熵产生得以保证。我们假设各向同性的分布，并对宏观场进行数值模拟，以评估动力学如何推动混合物向热平衡和化学平衡发展。我们表明，假设虚物种温度的等化只是确保经典H-Boltzmann函数单调性的合理假设。模拟显示，当初始温度远离平衡时，向平衡的松弛发生在后期阶段，经典H-Boltzmann函数在初始瞬态期间并不单调。
英文摘要：
We investigate numerically a recent BGK-type model for a multi-component mixture of monatomic gases, undergoing a reversible bimolecular chemical reaction. The model replaces each collisional term of the Boltzmann equation with a relaxation term, thereby describing separately the effects of the mechanical processes and the chemical reaction. Additionally, the model exhibits consistency properties. The correct entropy production is ensured when auxiliary temperatures in the chemical contributions share a common value. We assume isotropic distributions and perform numerical simulations for the macroscopic fields to appraise how the dynamics push the mixture toward thermalization and chemical equilibrium. We show that the hypothesis on the equalization of fictitious species temperatures is justifiable to ensure the monotonicity of the classical $H$-Boltzmann functional. Simulations show that, when initial temperatures are far from equilibrium, the relaxation towards equilibrium occurs at a later stage and the classical $H$-Boltzmann functional is not monotone during the initial transient.
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