## Abstract

Vector Fields occur in many of the problems in science and engineering. In combustion processes for instance, vector fields describe the flow of the gas. This process can be enhanced using vector field visualization techniques. Also wind tunnel experiments can be analyzed. An example is the design of an air wing. The wing can be optimized to crate a smoother flow around it. Vector field visualization methods help the engineer to detect critical features of the flow. Consequently, feature detection methods gained great importance during the last years.

Topological methods are often used to visualize vector fields because they clearly depict the structure of the vector field. In previous publications about topological methods closed streamlines are neglected. Since closed streamlines can behave in exactly the same way as sources and sinks they are an important feature that cannot be ignored anymore.

To accomplish this, this work concentrates on detecting this topological feature. We introduce a new algorithm that finds closed streamlines in vector fields that are given on a gird where the vectors are interpolated linearly. We identify regions that cannot be left by a streamline. According to the Poincare-Bendixson theorem there is a closed a streamline in such a region if it does not contain any critical point. Then we identify the exact location using the Poincare map. In contract to to other algorithms, this method does not presume the existence of a closed streamline. Consequently, this algorithm is able to really detect closed streamlines inside the vector field. A parallel version of this algorithm is also described to reduce computational time. The implementation scales reciprocally proportional to the CPU speed of the used computers.

In order to get a better understanding of closed streamlines we sketch the whole evolution of a closed streamline in time dependent flows. This results in a tube shaped visualization representing the closed streamline over time. The emerging and vanishing of the closed streamline can be easily investigated to get more insight into this feature.

In combustion processes closed streamlines in a three dimensional flow are a hint for recirculation zones. These zones describe regions inside the flow where the gas stays quite long. This is necessary for the gas to completely burn. Therefore, we also show how to detect this important feature in three dimensional vector fields.

Original language | American English |
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Qualification | Ph.D. |

State | Published - Jan 1 2002 |

## Disciplines

- Computer Sciences
- Engineering