Visualization Methods for Vortex Rings and Vortex Breakdown Bubbles

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.

[1]  Helwig Loffelmann,et al.  Visualizing Local Properties and Characteristic Structures of Dynamical Systems , 1998 .

[2]  Hans-Peter Seidel,et al.  Saddle connectors - an approach to visualizing the topological skeleton of complex 3D vector fields , 2003, IEEE Visualization, 2003. VIS 2003..

[3]  G. Tóth.  The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes , 2000 .

[4]  Charles D. Hansen,et al.  Visualization of intricate flow structures for vortex breakdown analysis , 2004, IEEE Visualization 2004.

[5]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[6]  D. Asimov.  Notes on the Topology of Vector Fields and Flows , 2003 .

[7]  Al Globus,et al.  A tool for visualizing the topology of three-dimensional vector fields , 1991, Proceeding Visualization '91.

[8]  Markus Rütten,et al.  Analyzing Vortex Breakdown Flow Structures by Assignment of Colors to Tensor Invariants , 2006, IEEE Transactions on Visualization and Computer Graphics.

[9]  Fotis Sotiropoulos,et al.  Chaotic advection in three-dimensional stationary vortex-breakdown bubbles: šil'nikov's chaos and the devil's staircase , 2001, Journal of Fluid Mechanics.

[10]  J. Norbury,et al.  A family of steady vortex rings , 1973, Journal of Fluid Mechanics.

[11]  James D. Meiss,et al.  Transport in Hamiltonian systems , 1984 .

[12]  Lambertus Hesselink,et al.  Representation and display of vector field topology in fluid flow data sets , 1989, Computer.

[13]  Filip Sadlo,et al.  Topology-guided Visualization of Constrained Vector Fields , 2007, Topology-based Methods in Visualization.

[14]  P. Roe,et al.  Divergence- and curl-preserving prolongation and restriction formulas , 2002 .

[15]  G. Pedrizzetti,et al.  Vortex Dynamics , 2011 .

[16]  Filip Sadlo,et al.  Flow Topology Beyond Skeletons: Visualization of Features in Recirculating Flow , 2009, Topology-Based Methods in Visualization II.

[17]  Andreas Spohn,et al.  Experiments on vortex breakdown in a confined flow generated by a rotating disc , 1998, Journal of Fluid Mechanics.

[18]  Dinshaw Balsara,et al.  A Comparison between Divergence-Cleaning and Staggered-Mesh Formulations for Numerical Magnetohydrodynamics , 2003 .

[19]  Xavier Tricoche,et al.  Tracking of vector field singularities in unstructured 3D time-dependent datasets , 2004, IEEE Visualization 2004.

[20]  Helwig Löffelmann,et al.  Visualizing Dynamical Systems near Critical Points , 1998 .

[21]  Xavier Tricoche,et al.  Surface techniques for vortex visualization , 2004, VISSYM'04.

[22]  Lukas Mroz,et al.  Case study: visualizing various properties of dynamical systems , 1998, Other Conferences.