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Asymetric Tensor Analysis for Flow VisualizationEugene Zhang, Harry Yeh, Zhongzang Lin, and Robert S. Laramee Paper (PDF, 4.84Mb). This material is based upon work supported by the National Science Foundation under Grant No. CCF0546881. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF). AbstractThe gradient of a velocity vector field is an asymmetric tensor
field which can provide critical insight that is difficult to infer To illustrate the structures in asymmetric tensor fields, we
introduce the notions of eigenvalue manifold and
eigenvector manifold. These concepts afford a number of theoretical
results that clarify the connections between symmetric and 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 tensordriven 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. Figures1. Flow visualization techniques based on arrow plot (a), vector field magnitude (b), vector field topology (c), and our tensordriven techniques: eigenvaluebased segmentation overlaid with vector field visualization (d), eigenvector analysis where colord indicating real and complex domains (e), and eigenvector analysis overlaid with eigenvalue analysis (f). Tensordriven flow visualization provides additional and complementary insights of the flow field.
2. Diesel engine simulation using an eigenvaluebased method (left) and a hybrid method (right).
3. Our technique is applied to the cooling jacket simulation data. Notice the flow and geometry are extremely complex.
