Automatic detection of open and closed separation and attachment lines

Kenwright,

doi:10.1109/visual.1998.745297

Cited by 55 publications

(36 citation statements)

References 14 publications

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“…In addition to the definition and computation of vortex core lines (see [8] for a bibliography), several authors have attempted to detect and display separation and attachment lines on surfaces. The major contribution in this field was made by Kenwright [6] who proposed a method that looks for the presence of separation lines on a cell-wise basis. Upon the assumption of local linearity of the flow a section of separation line is extracted in each triangle as the intersection of specific lines present in the phase portrait of a first-order critical point with the interior of the cell.…”

Section: Related Workmentioning

confidence: 99%

Extraction of Separation Manifolds using Topological Structures in Flow Cross Sections

Wiebel

Tricoche

Scheuermann

2009

Mathematics and Visualization

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Summary: The study of flow separation from walls or solid objects is still an active research area in the fluid dynamics and flow visualization communities and many open questions remain. This paper aims at introducing a new method for the extraction of separation manifolds originating from separation lines. We address the problem from the flow visualization side by investigating features in flow cross sections around separation lines. We use the topological signature of the separation in these sections, in particular the presence of saddle points and their separatrices, as a guide to initiate the construction of the separation manifolds. Having this first part we use well known stream surface construction methods to propagate the surface further into the flow. Additionally, we discuss some lessons learned in the course of our experimentation with well known and new ideas for the extraction of separation lines.

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Section: Related Workmentioning

confidence: 99%

Extraction of Separation Manifolds using Topological Structures in Flow Cross Sections

Wiebel

Tricoche

Scheuermann

2009

Mathematics and Visualization

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“…Before describing these elements, we briefly review the concepts of attachment and separation points by Kenwright [40]. Given a vector field V and a point p 0 in the plane, we consider the following values: e 1 Â u and e 2 Â u, where u is the vector value at p 0 , and e 1 and e 2 are the major and minor eigenvectors of the Jacobian.…”

Section: Attracting and Repelling Basis Vector Fieldsmentioning

confidence: 99%

Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition

Chen

Mischaikow

Laramee

et al. 2007

IEEE Trans. Visual. Comput. Graphics

105

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Abstract-Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper, we provide a new technique that allows for the systematic creation and cancellation of fixed points and periodic orbits. This technique enables vector field design and editing on the plane and surfaces with desired qualitative properties. The technique is based on Conley theory, which provides a unified framework that supports the cancellation of fixed points and periodic orbits. We also introduce a novel periodic orbit extraction and visualization algorithm that detects, for the first time, periodic orbits on surfaces. Furthermore, we describe the application of our periodic orbit detection and vector field simplification algorithms to engine simulation data demonstrating the utility of the approach. We apply our design system to vector field visualization by creating data sets containing periodic orbits. This helps us understand the effectiveness of existing visualization techniques. Finally, we propose a new streamline-based technique that allows vector field topology to be easily identified.

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“…The gradient tensor has found applications in a wide range of vector field visualization tasks such as fixed point classification and separatrix computation [12], attachment and separation line extraction [17], vortex core identification [29], [16], [25], [27], and periodic orbit detection [4]. However, the use of the gradient tensor in these applications is often limited to point-wise computation and analysis.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Tensor Analysis for Flow Visualization

Zhang

Yeh

Lin

et al. 2009

IEEE Trans. Visual. Comput. Graphics

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Abstract-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 that can represent either a 2D compressible flow or the projection of a 3D compressible or incompressible flow onto a 2D manifold. 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 antisymmetric components in tensor fields. In addition, these manifolds naturally lead to partitions of tensor fields, which we use to design effective visualization strategies. Moreover, we extend eigenvectors continuously into the complex domains which we refer to as pseudoeigenvectors. We make use of evenly spaced tensor lines following pseudoeigenvectors to illustrate the local linearization of tensors everywhere inside complex domains simultaneously. 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 a 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.

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Automatic detection of open and closed separation and attachment lines

Cited by 55 publications

References 14 publications

Extraction of Separation Manifolds using Topological Structures in Flow Cross Sections

Extraction of Separation Manifolds using Topological Structures in Flow Cross Sections

Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition

Asymmetric Tensor Analysis for Flow Visualization

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