Asymmetric tensor analysis for flow visualization.
The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectory-based vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these structures can be used to infer the behaviors of the velocity field. To illustrate the structures in asymmetric tensor fields, we introduce the notions of eigenvalue and eigenvector manifolds. These concepts afford a number of theoretical results that clarify the connections between symmetric and antisymmetric components in tensor fields. In addition, these manifolds naturally lead to partitions of tensor fields, which we use to design effective visualization strategies. Both eigenvalue manifold and eigenvector manifold are supported by a tensor reparameterization with physical meaning. This allows us to relate our tensor analysis to physical quantities such as rotation, angular deformation, and dilation, which provide physical interpretation of our tensor-driven vector field analysis in the context of fluid mechanics. To demonstrate the utility of our approach, we have applied our visualization techniques and interpretation to the study of the Sullivan Vortex as well as computational fluid dynamics simulation data.
Zhang
Eugene
E
School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331, USA. zhange@eecs.oregonstate.edu
Yeh
Harry
H
Lin
Zhongzang
Z
Laramee
Robert S
RS
D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008962:Models, Theoretical; D014584:User-Computer Interface