Issue No. 06 - November/December (2007 vol. 13)
Xavier Tricoche , IEEE
The recently introduced notion of Finite-Time Lyapunov Exponent to characterize Coherent Lagrangian Structures provides a powerful framework for the visualization and analysis of complex technical flows. Its definition is simple and intuitive, and it has a deep theoretical foundation. While the application of this approach seems straightforward in theory, the associated computational cost is essentially prohibitive. Due to the Lagrangian nature of this technique, a huge number of particle paths must be computed to fill the space-time flow domain. In this paper, we propose a novel scheme for the adaptive computation of FTLE fields in two and three dimensions that significantly reduces the number of required particle paths. Furthermore, for three-dimensional flows, we show on several examples that meaningful results can be obtained by restricting the analysis to a well-chosen plane intersecting the flow domain. Finally, we examine some of the visualization aspects of FTLE-based methods and introduce several new variations that help in the analysis of specific aspects of a flow.
flow visualization, feature detection, 3D vector field visualization
C. Garth, F. Gerhardt, X. Tricoche and H. Hans, "Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications," in IEEE Transactions on Visualization & Computer Graphics, vol. 13, no. , pp. 1464-1471, 2007.