TY - GEN A1 - Kuhn, Alexander A1 - Engelke, Wito A1 - Rössl, Christian A1 - Hadwiger, Markus A1 - Theisel, Holger T1 - Time Line Cell Tracking for the Approximation of Lagrangian Coherent Structures with Subgrid Accuracy N2 - Lagrangian Coherent Structures (LCS) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the Finite Time Lyapunov Exponent (FTLE) field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieves subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its benefits and limitations. T3 - ZIB-Report - 13-71 KW - time-dependent vector fields KW - flow field visualization KW - Lagrangian Coherent Structures (LCS) KW - finite-time Lyapunov exponents (FTLE) KW - time lines Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43050 SN - 1438-0064 ER - TY - GEN A1 - Kuhn, Alexander A1 - Engelke, Wito A1 - Flatken, Markus A1 - Hege, Hans-Christian A1 - Hotz, Ingrid T1 - Topology-based Analysis for Multimodal Atmospheric Data of Volcano Eruptions N2 - Many scientific applications deal with data from a multitude of different sources, e.g., measurements, imaging and simulations. Each source provides an additional perspective on the phenomenon of interest, but also comes with specific limitations, e.g. regarding accuracy, spatial and temporal availability. Effectively combining and analyzing such multimodal and partially incomplete data of limited accuracy in an integrated way is challenging. In this work, we outline an approach for an integrated analysis and visualization of the atmospheric impact of volcano eruptions. The data sets comprise observation and imaging data from satellites as well as results from numerical particle simulations. To analyze the clouds from the volcano eruption in the spatiotemporal domain we apply topological methods. Extremal structures reveal structures in the data that support clustering and comparison. We further discuss the robustness of those methods with respect to different properties of the data and different parameter setups. Finally we outline open challenges for the effective integrated visualization using topological methods. T3 - ZIB-Report - 16-03 KW - multi-modal, intergrated data analysis, topology Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57043 SN - 1438-0064 ER -