Helman, J.L., Hesselink, L.: Visualizing vector field topology in fluid flows. IEEE Computer Graphics & Applications 11(3), 36--46 (May 1991)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Methodology and Techniques I.6.6 [Simulation and Modeling] Simulation Output Analysis. Additional Keywords: multi level visualization techniques, flow visualization, flow topology 1 Introduction Helman and Hesselink introduced the concept of vector field topology in flow visualization, [1]. Flow topology combines the simplicity of schematic depictions with the quantitative accuracy of curves computed directly from the data. Topology visualization captures the essential features when applied to simple flow fields. For complex flows, however, the large number of critical points ....

....involved in collapsing topologies. Finally, in section 5 we apply the technique to a complex application: the visualization of skin friction on a square cylinder in a turbulent flow field. 2 Related work The visualization of vector field topology has been introduced by Helman and Hesselink, [1]. The topology presents essential information of a flow field by partitioning it in regions using critical points connected by streamlines. Critical points are points in the flow where the velocity magnitude is equal to zero. Each critical point is classified based on the behavior of the flow ....

J.L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36--46, May 1991.

....component are an exact decomposition of the vector field containing all information. 1 Introduction and Related Work Singularities of vector fields are among the most important features of flows. They determine the physical behavior of flows and allow one to characterize the flow topology [9][10]. The most prominent singularities are sinks, sources, and vortices. Higher order singularities often appear in magnetic fields. All these singularities must be detected and analyzed in order to understand the physical behavior of a flow or in order to use them as an ingredient for many ....

J. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics & Applications, 11(3):36--46, 1991.

....critical points to be non degenerate, i.e. regular. Saddle points are characterized by two real eigenvalues of with opposite sign, whereas at vortices we obtain complex conjugate eigenvalues with vanishing real part. Stagnation points on are similar to saddles. For details we refer to [7]. In each topological region there is a family of periodic orbits close to the heteroclinic, respectively homoclinic orbit. This observation gives reason for the following segmentation algorithm. At first, we search for critical points in and stagnation points on ; We calculate the ....

J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE G&A, 11 (3):36--46, 1991.

....Blue represents lower velocities than red. The illumination model for curves of Banks [12] is used in the rendering, providing a better sense of curvature. 2.3 Topology Techniques Topological techniques can be quite effective in capturing the global features of a flow field. Helman and Hesslink [29] proposed to analyze the vector field topology based on critical point classification, which has been widely used to analyze solution trajectories of ordinary differential equations. Critical points are points that have zero vector magnitude. In two dimensional flow fields, they can be found ....

Helman, J.L. and L. Hesselink, Visualizing vector field topology in fluid flows. IEEE Computer Graphics & Applications, May 1991. 11 (3): p. 36-46.

....by the Jacobian tensor u . Critical points are classified, to a first order approximation, by the eigenvalues and eigenvectors of u . The two dimensional topology of a vector field is constructed by finding the set of streamlines that start or end at critical points. Helman and Hesselink [Hel91] and Globus et al. Glo91] showed that (closed) separation lines could be generated by 2 integrating outwards from the saddle critical points in the real eigenvector directions. These tangent curves were classified as either separation or reattachment lines based on the sign of the eigenvalues: ....

....vector field topology (upper) local phase plane analysis (center) and global vector field topology with critical point at infinity (lower) 4 Singular streamlines were extracted from the analytical vector field using one of three techniques. The first was linear vector field topology [Hel91], the second was local phase plane analysis [Ken99] and the third was global vector field topology (Section 3) The results shown in Figure 2 exemplify the differences between these techniques. The linear vector field topology method only identifies singular streamlines that originate or ....

J. Helman and L. Hesselink, Visualizing vector field topology in fluid flows, IEEE Computer Graphics and Applications, Vol. 11, no. 3, pp. 36-46, May 1991.

.... Coordinated Modeling Center (CCMC) BATS R US is a 3D magnetohydrodynamics (MHD) code developed at the University of Michigan for massively parallel computers using adaptive mesh refinement (AMR) 1] Critical point analysis is an important technique utilized in vector field visualization [2, 3, 4, 5]. Critical points are points at which the magnitude of the vector field vanishes and can used to accurately represent the important aspects of the vector field topology. Recently Wong et al. 6] proposed a vorticity based filtering technique to eliminate less interesting and sometimes ....

James L Helman,. and Lambertus Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36-46, May 91.

....from BATS R US is stored in the HDF5 [15] format in a manner similar to ChomboVis [6] In the next section, we describe a method for vector field visualization of 3D AMR data. 3. Visualization Strategy Critical point analysis is an important technique utilized in vector field visualization [2, 3, 5, 9, 10, 12, 13]. Critical points are points at which the magnitude of the vector field vanishes and can used to accurately represent the important aspects of the vector field topology. Parnell et al. 8] provides the physical theoretical structure of magnetic neutral points. SWX uses OpenDX [14] for ....

James L Helman, and Lambertus Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36-46, May 91.

....obtain, especially in 3D. The work by Abraham and Shaw in 1992 [1] is one of the seldom exceptions which impressingly demonstrate the worth of such (hand drawn) illustrations. Other attempts to use the information gained from flow analysis can be found in literature: in 1991, Helman and Hesselink [9] proposed to visualize the geometry of the topological structure for flow data originating in flow simulation. Fixed points, detachment attachment points, separatrices, etc. are visualized. Also, the information obtained from the analysis of the Jacobian matrix at fixed points is used for ....

J. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics & Applications, 11(3):36--46, 1991.

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Helman, J.L., Hesselink, L.: Visualizing vector field topology in fluid flows. IEEE Computer Graphics & Applications 11(3), 36--46 (May 1991)

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J. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36--46, 1991.

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J. L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36--46, May/Jun. 1991.

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J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE Computer Graphics and Applications, 11(3):36--46, May 1991.

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J. L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36--46, May/Jun. 1991.

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J. Helman and L. Hesselink, Visualizing vector field topology in fluid flows, IEEE Computer Graphics and Applications, Vol. 11, no. 3, pp. 36-46, May 1991.

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J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE Computer Graphics and Applications, 11(3):36-- 46, May 1991.

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J. L. Helman and L. Hesselink, "Visualizing vector field topology in fluid flows," IEEE Comput. Graphics Applicat., vol. 11, pp. 36--46, May. 1991.

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J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE Computer Graphics and Applications, 11(3):36-- 46, May 1991.

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J. L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE CG&A, 11(3):36--46, May 1991.

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J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE Computer Graphics and Applications, 11(3):36-- 46, May 1991.

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James Helman and Lambertus Hesselink. Visualizing vector field topology in fluid flows. Computer Graphics and Applications, 11(3):36--46, May 1991.

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J.L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36--46, May 1991.

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James L. Helman, and Lamberms Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, Vol. 11, No.3, May, pp.36-46, 1991.

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J.L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36-46, 1991.

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James L. Helman and Lambertus Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics & Applications, 11(3):36--46, May 1991.

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James L. Helman and Lambertus Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36--46, May 1991. 13, 15

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