Glyph-Based Multiscale Visualization of Turbulent Multi-Physics Statistics

TL;DR

This work tackles the challenge of visualizing multivariate, multiscale turbulent multi-physics data in an integrated view. It introduces a pipeline that combines curvelet-based multiscale decomposition, level-set restricted centroidal Voronoi tessellation (LSRCVT) for spatial partitioning, and glyph-based encodings to summarize local statistics around flow features in a 3D visualization with linked 2D views. Key contributions include a scalable LSRCVT-based aggregation framework for multiscale multivariate data, two glyph designs for cross-field and cross-scale analysis, and demonstrations on turbulent combustion and channel-flow datasets with performance metrics and data reduction results. The proposed approach enables researchers to analyze cross-scale interactions in turbulent flows and thermo-chemical processes more efficiently, with potential impact on combustion modeling and turbulence analysis.

Abstract

Many scientific and engineering problems involving multi-physics span a wide range of scales. Understanding the interactions across these scales is essential for fully comprehending such complex problems. However, visualizing multivariate, multiscale data within an integrated view where correlations across space, scales, and fields are easily perceived remains challenging. To address this, we introduce a novel local spatial statistical visualization of flow fields across multiple fields and turbulence scales. Our method leverages the curvelet transform for scale decomposition of fields of interest, a level-set-restricted centroidal Voronoi tessellation to partition the spatial domain into local regions for statistical aggregation, and a set of glyph designs that combines information across scales and fields into a single, or reduced set of perceivable visual representations. Each glyph represents data aggregated within a Voronoi region and is positioned at the Voronoi site for direct visualization in a 3D view centered around flow features of interest. We implement and integrate our method into an interactive visualization system where the glyph-based technique operates in tandem with linked 3D spatial views and 2D statistical views, supporting a holistic analysis. We demonstrate with case studies visualizing turbulent combustion data--multi-scalar compressible flows--and turbulent incompressible channel flow data. This new capability enables scientists to better understand the interactions between multiple fields and length scales in turbulent flows.

Figures (10)

• Figure 1: Fields $\mathbf{X}_i$ are input to the scale decomposition, and surface features are input to the LSRCVT. Aggregation of spectral energy is done for each scale of each field based on the LSRCVT regions. Glyphs are generated interactively based on the aggregated data. The top two glyphs show the strength glyph design, the left encoding mean spectral energy for 1 field and 3 scale bins, and the right encoding spectral energy for 5 fields and 3 scale bins. The one below the two shows the starplot glyph encoding 5 fields and 1 scale bin.
• Figure 2: Isosurfaces of a scale decomposition: (left to right) input field, large, medium, then small scales.
• Figure 3: (Left) Border artifacts introduced after spectral filtering. (Right) Artifacts resolved by using overlapping windowed blocks.
• Figure 4: A 2D LSRCVT using the distance field. (Left) The darker region highlights band $B_{a,b}$. $C_{a,b}^k$ denotes a component of $B_{a,b}$. (Right) Elements in $R_s$, where $R_s \subset C_{a,b}^k \subset B_{a,b}$, are aggregated. The aggregate data can be encoded as a glyph centered at site $s$.
• Figure 5: The two visualizations show the same information, spectral energy contribution of the highest frequencies for 3 variables, using the starplot glyph (left) and strength glyph (right). The user can interactively switch between the two glyph types. The top two glyphs on the right show averages over all glyphs. While color-based encoding makes it easy to see variation from afar, a user's perceptual mapping between colors to values can be more complex or error-prone since it requires referencing color legends, and depends on the user's color perception. Distance-based value encoding tends to be perceived more intuitively and precisely. The bottom two glyphs show mean spectral energy for 3 variables and 3 scale bins. Using separate color maps for each variable makes it easier to tell different variables apart at a glance, but makes comparing values across variables more difficult. The bottom glyph uses the same color map for all 3 variables to make comparison easier.