Measuring Complexity in Lagrangian and Eulerian Flow Descriptions

• Published in: Computer graphics forum 2010-09, Vol.29 (6), p.1783-1794
• Main Authors: Jänicke, H., Scheuermann, G.
• Format: Article
• Language: English
• Subjects: Complexity; Complexity theory; Computational fluid dynamics; Computer graphics; Datasets; Descriptions; Dynamics; flow visualization; Fluid dynamics; Fluid flow; frame of reference; I.6.6 [Simulation and Modeling]: Simulation Output Analysis; Information theory; Intervals; J.2 [Physical Sciences and Engineering]: Mathematics and Statistics; Lagrange multiplier; statistical complexity; Studies; Temporal logic; time-dependent data; Visualization
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/j.1467-8659.2010.01648.x

Automatic detection of relevant structures in scientific data sets is still one of the big challenges in visualization. Techniques based on information theory have shown to be a promising direction to automatically highlight interesting subsets of a time‐dependent data set. The methods that have been proposed so far, however, were restricted to the Eulerian view. In the Eulerian description of motion, a position fixed in space is observed over time. In fluid dynamics, however, not only the site‐specific analysis of the flow is of interest, but also the temporal evolution of particles that are advected through the domain by the flow. This second description of motion is called the Lagrangian perspective. To support these two different frames of reference widely used in CFD research, we extend the notion of local statistical complexity (LSC) to make them applicable to Lagrangian and Eulerian flow descriptions. Thus, coherent structures can be identified by highlighting positions that either feature unusual temporal dynamics at a fixed position or that hold a particle that experiences such dynamics while passing through the position. A new area of application is opened by LagrangianLSC, which can be applied to short pathlines running through each position in the data set, as well as to individual pathlines computed for longer time intervals. Coloring the pathline according to the local complexity helps to detect extraordinary dynamics while the particle passes through the domain. The two techniques are explained and compared using different fluid flow examples.