通过线性化松弛再分布方法逼近多尺度动力系统中的慢动力学与快动力学
Approximation of slow and fast dynamics in multiscale dynamical systems by the linearized Relaxation Redistribution Method
AI总结：
本文提出线性化松弛再分布方法，通过虚拟快速弛豫动力学将任意维度慢不变流形构造转化为刚性ODE求解，并用于氢空气燃烧详细机理。
摘要：
本文引入一种虚拟动力学，用于描述刚性常微分方程（ODE）系统向相空间中稳定低维不变流形（慢不变流形，SIM）的唯一快速弛豫过程。由此，构造任意维度SIM这一高难度问题，被转化为显著更简单的任务：利用文献中已有的刚性数值格式求解一个经过适当设计的ODE系统。本着同样的思路，本文阐述了用于局部构造快子空间的一组方程，并讨论了上述方程可能的初始化过程。该方法已在氢气与空气燃烧的详细反应机理上完成实现，同时采用一个具有不变性方程精确Chapman–Enskog解的模型作为基准。
英文摘要：
In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold - SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE system by stiff numerical schemes available in the literature. In the same spirit, a set of equations is elaborated for local construction of the fast subspace, and possible initialization procedures for the above equations are discussed. The implementation to a detailed mechanism for combustion of hydrogen and air has been carried out, while a model with the exact Chapman-Enskog solution of the invariance equation is utilized as a benchmark.
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