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Keywords
Institute
Time-dependent vector fields are of high relevance to describe a wide range
of physical phenomena based on particle motion, including stall effects in
technical engineering, blood flow anomalies, and atmospheric mass trans-
port. The efficient analysis and fundamental understanding of intrinsic field
properties can lead to significant improvements when interacting with such
phenomena based on the available field data. So called Lagrangian methods
are a particularly established technique for this purpose. They are based on
the evaluation of time-dependent particle trajectories.
This work will present an overview of the state of the art in time-dependent
vector field analysis and visualization, with special focus on topology-oriented
and Lagrangian methods. The first core aspect of this work is the introduction
of a novel concept for a more objective and qualitative benchmark of existing
Lagrangian approaches. Based on this benchmark, this work contributes
and evaluates a set of novel concepts, that offer new perspectives towards
established approaches with respect to computational handling, quality and
efficiency. The second core aspect is the empirical application and validation
of Lagrangian methods with respect to practically relevant analysis scenarios.
Each application case includes an introduction into the underlying problem
statement and an efficient solution using Lagrangian methods. The validation
focuses on the comparison with existing flow analysis concepts and aspects
of the quantitative evaluation in each case. Together, both topics of this work
contribute towards a more consistent formalization, but also to the improved
applicability of Lagrangian methods.