Flow Visualization and Analysis: From Geometry to Physics

As the size and complexity of flow data sets continuously increase, many vector field visualization techniques aim to generate an abstract representation of the geometric characteristics of the flow to simplify its interpretation. However, most of the geometric-based visualization techniques lack the ability to reveal the physically important features. Additional efforts are needed to interpret the physical characteristics from the geometric representation of the flow. In this work, the Lagrangian accumulation framework is introduced first, which accumulates various local physical and geometric properties of individual particles along the associated integral curves. This accumulation process results in a number of attribute fields that encode the information of certain global behaviors of particles, which can be used to achieve an abstract representation of the flow data. This framework is utilized to aid the classification of integral curves, produce texture-based visualizations, study property transport structures, and identify discontinuous behaviors among neighboring integral curves. Although the accumulation framework is simple and effective, the detailed flow behavior at individual integration points (and times) along the integral curves is suppressed, leading to incomplete analysis and visualization of flow data. In order to achieve a more detailed exploration, a new flow-exploration framework is investigated based on the time-series data or Time Activity Curves (TAC) of local properties. In this framework, the physical behavior of the individual particles can be described via their respective TACs. An event detector based on TACs is proposed to capture the local and global similarity of any spatial point with its neighboring points with a new dissimilarity metric. A hierarchical clustering framework is then developed based on this metric, upon which a level-of-detail representation of the flow can be obtained. This new framework is applied to a number of 2D and 3D unsteady-flow data sets to demonstrate its effectiveness.