Comparative Visual Analysis of Lagrangian Transport in CFD Ensembles

Abstract

Fig. 1. An ensemble of a 2D convection flow field is analyzed using the proposed joint variance visualization techniques. From left to right: Individual variances of four of the data set runs show high variances around the heating cylinder. Brushing in the classification space allows for the identification of similar (green), dissimilar (red), and uncertain regions (blue and white). Together with a color mapped visualization of the ensemble domain and interactive pathline seeding, a complete analysis of transport is possible.Abstract-Sets of simulation runs based on parameter and model variation, so-called ensembles, are increasingly used to model physical behaviors whose parameter space is too large or complex to be explored automatically. Visualization plays a key role in conveying important properties in ensembles, such as the degree to which members of the ensemble agree or disagree in their output. For ensembles of time-varying vector fields, there are numerous challenges for providing an expressive comparative visualization, among which is the requirement to relate the effect of individual flow divergence to joint transport characteristics of the ensemble. Yet, techniques developed for scalar ensembles are of little use in this context, as the notion of transport induced by a vector field cannot be modeled using such tools. We develop a Lagrangian framework for the comparison of flow fields in an ensemble. Our techniques evaluate individual and joint transport variance and introduce a classification space that facilitates incorporation of these properties into a common ensemble visualization. Variances of Lagrangian neighborhoods are computed using pathline integration and Principal Components Analysis. This allows for an inclusion of uncertainty measurements into the visualization and analysis approach. Our results demonstrate the usefulness and expressiveness of the presented method on several practical examples.

A Survey of Colormaps in Visualization

“…The colormaps are adopted for the comparison task within a spaghetti plots and across different simulation runs. Hummel et al [51] design a 2D interactive colormap to separate the joint variance parameter space into similar, dissimilar and uncertain regions to visualize and explore an ensemble of 2D convection flows. The interactivity of the colormap enables the user to visualize specific values of interest.…”

Comparative visualization of vector field ensembles based on longest common subsequence

“…To quantify the linearized deformation presented in Lagrangian neighborhood for each fixed locations in ensemble fields, Hummel et al [10] proposed a PCA-based method for computational fluid dynamics simulations. This method can evaluate both individual and joint transport variance to reveal the characteristics of the ensembles.…”

“…The first is pointwise Euclidean distance [7,22] (we abbreviate it to pointwise distance in this paper). The other is linearized deformation measure [10] on vector field ensembles. The pointwise method defines the distance between ensemble pathlines by accumulating their pointwise distances along timesteps.…”

“…Furthermore, the exaggerated and unpredictable distances substantially enlarge the distribution range of the distance between ensemble pathlines, resulting in data in higher dynamic range. In addition to the pointwise method, a new metric [10] was proposed to measure linearized deformation within a given Lagrangian neighborhood in ensemble vector fields. It employs the principal component analysis (PCA) to measure shape deformations for computational fluid dynamics simulations.…”

Comparative visualization of multiple time surfaces by planar surface reformation

“…Schlemmer et al [34] instead focused on the feature-level comparison of 2D flows, using invariant moments as feature descriptors. Hummel et al [19] proposed to use visual analysis tools, such as linking-and-brushing for the comparison of ensembles of CFD simulations. Angelelli and Hauser [1] proposed a method for straightening 3D tubular flow data (e.g., arterial blood flow) in order to facilitate image-level comparisons.…”