On slow manifolds of chemically reactive systems
On slow manifolds of chemically reactive systems
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DOI：
10.1063/1.1485959
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发表时间：
2002-07
影响因子：
4.4
通讯作者：
Sandeep Singh;J. M. Powers;S. Paolucci
中科院分区：
文献类型：
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作者：
Sandeep Singh;J. M. Powers;S. Paolucci
这项工作解决了化学反应流的慢流形的构造问题。这种构造依赖于局部特征系统的相同分解，该局部特征系统用于形成所谓的固有低维流形（ILDM）。我们首先阐明标准 ILDM 近似对模拟空间均匀反应系统的常微分方程组的准确性。结果表明，ILDM 实际上只是同一系统的更基本的慢不变流形 (SIM) 的近似。随后，我们将标准 ILDM 方法改进扩展到反应与对流和扩散耦合的系统。通过平衡紧密耦合的反应/对流/扩散系统的快速动力学并仅求解同一系统的慢速动力学来获得简化模型方程，以降低计算成本，同时保持所需的精度水平。该改进是通过制定椭圆来实现的...
This work addresses the construction of slow manifolds for chemically reactive flows. This construction relies on the same decomposition of a local eigensystem that is used in formation of what are known as Intrinsic Low Dimensional Manifolds (ILDMs). We first clarify the accuracy of the standard ILDM approximation to the set of ordinary differential equations which model spatially homogeneous reactive systems. It is shown that the ILDM is actually only an approximation of the more fundamental Slow Invariant Manifold (SIM) for the same system. Subsequently, we give an improved extension of the standard ILDM method to systems where reaction couples with convection and diffusion. Reduced model equations are obtained by equilibrating the fast dynamics of a closely coupled reaction/convection/diffusion system and resolving only the slow dynamics of the same system in order to reduce computational costs, while maintaining a desired level of accuracy. The improvement is realized through formulation of an ellipt...