Stability of Dissipation Elements: A Case Study in Combustion
Stability of Dissipation Elements: A Case Study in Combustion
复制标题
耗散元件的稳定性：燃烧案例研究
DOI：
10.1111/cgf.12361
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发表时间：
2014
影响因子：
2.5
通讯作者：
Valerio Pascucci
中科院分区：
文献类型：
--
作者：
A. Gyulassy;P. Bremer;R. Grout;H. Kolla;Jacqueline H. Chen;Valerio Pascucci
近年来，耗散元件作为测量湍流基本性质的一种手段，如湍流长度尺度和分区，越来越受到人们的欢迎。耗散单元根据标量函数f：→ f的梯度流场中流线的源和目的地来分割区域。传统上，通过在正梯度方向和负梯度方向上从每个体素的中心对流线进行数值积分，并将流线终止于相同极值对的那些体素分组来计算它们。我们表明，同样的结构映射以及最近开发的可视化社区的组合拓扑概念。也就是说，耗散元对应于莫尔斯-斯梅尔复形的胞元集合。基于拓扑的公式能够对耗散元件的性质进行更探索性的分析，特别是在理解它们相对于小尺度变化的稳定性方面。我们提出了两个燃烧科学的例子，提出了小尺度扰动的作用，甚至耗散元素本身的定义的重要问题。
Recently, dissipation elements have been gaining popularity as a mechanism for measurement of fundamental properties of turbulent flow, such as turbulence length scales and zonal partitioning. Dissipation elements segment a domain according to the source and destination of streamlines in the gradient flow field of a scalar function f : → ℝ. They have traditionally been computed by numerically integrating streamlines from the center of each voxel in the positive and negative gradient directions, and grouping those voxels whose streamlines terminate at the same extremal pair. We show that the same structures map well to combinatorial topology concepts developed recently in the visualization community. Namely, dissipation elements correspond to sets of cells of the Morse‐Smale complex. The topology‐based formulation enables a more exploratory analysis of the nature of dissipation elements, in particular, in understanding their stability with respect to small scale variations. We present two examples from combustion science that raise significant questions about the role of small scale perturbation and indeed the definition of dissipation elements themselves.