The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Divergence- and curl-preserving prolongation and restriction formulas
Journal of Computational Physics
A tool for visualizing the topology of three-dimensional vector fields
VIS '91 Proceedings of the 2nd conference on Visualization '91
Visualization of Intricate Flow Structures for Vortex Breakdown Analysis
VIS '04 Proceedings of the conference on Visualization '04
Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets
VIS '04 Proceedings of the conference on Visualization '04
Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Analyzing Vortex Breakdown Flow Structures by Assignment of Colors to Tensor Invariants
IEEE Transactions on Visualization and Computer Graphics
Surface techniques for vortex visualization
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Topologically relevant stream surfaces for flow visualization
Proceedings of the 25th Spring Conference on Computer Graphics
Magnetic Flux Topology of 2D Point Dipoles
Computer Graphics Forum
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Vortex breakdown bubbles are a subject which is of interest in many disciplines such as aeronautics, mixing, and combustion. Existing visualization methods are based on stream surfaces, direct volume rendering, tensor field visualization, and vector field topology. This paper presents a topological approach which is more closely oriented at the underlying theory of continuous dynamical systems. Algorithms are described for the detection of vortex rings and vortex breakdown bubbles, and for visualization of their characteristic properties such as the boundary, the chaotic dynamics, and possible islands of stability. Since some of these require very long streamlines, the effect of numerically introduced divergence has to be considered. From an existing subdivision scheme, a novel method for divergence conserving interpolation of cuboid cells is derived, and results are compared with those from standard trilinear interpolation. Also a comparison of results obtained with and without divergence cleaning is given.