Norman J. Zabusky and Deborah Silver, Laboratory for Visiometrics and Modeling, Mechanical & Aerospace Engineering & CAIP Center, Rutgers, The State University of New Jersey
The goal of large-scale simulations and experiments in computational science and technology is a quantitative and mathematical understanding for the model being investigated. We are employing the visiometrics and modeling paradigm. Visiometrics involves two categories of related processes:
- Visualization (including data projection, image rendering, feature extraction and classification), and
- Quantification (or feature measurement, space-time feature identification, and feature tracking).
Visualization involves projecting the data into alternate spaces (e.g. wave number space for spectra) or lower dimensional spaces (e.g. space-time diagrams), rendering the features, and isolating observed coherent" regions. Examples of coherent structures from fluid dynamics include: wave packets; shock waves; solitons; eddies; holes; bubbles; rings; tubes; spikes; etc.
Quantification involves measuring properties of coherent features (or objects) that are defined according to a physically based rule or that lie above some threshold. This includes: content (volume, mass, charge. circulation, etc. ); moments about extrema (e.g. quadratic forms of thresholded objects); gradients, curvatures, torsion's of skeletons of tubular or layered domains; critical points of velocity fields; eigenvalues and eigenvectors of tensor fields, etc.; and properties of space-time trajectories of these objects in the original or lower-dimensional (projected) spaces.
We are developing tools to easily access, manipulate, extract, track and archive essential features of one or more computer simulations, or laboratory or field experiments. The cogent assimilation and juxtaposition of measured and simulated data sets and their thresholded projections into lower dimensions will provide insights into the causes of observed phenomena. These insights will show the way toward formulating hierarchies of mathematical models and will result in increased reliability of predictions.
Areas of interest include novel algorithms to manage, visualize and quantify massive data sets using numerical, geometrical and graphical techniques. Quantification encompasses identifying coherent regions and structures, extracting these regions, simplifying them and fitting terse mathematical descriptions to them. Parallel algorithms for visualizing, quantifying, and managing hierarchical datasets are being developed.
Direct numerical simulations in computational fluid dynamics provide the data sets for these studies, including simulations done on a CRAY Y/MP and C-90 at PSC and the Connection Machine CM5 at NCSA. We are presently studying: 2D and 3D shock-interface and shock-bubble interactions and compressible coherent structures and turbulence; and 2D vortex dynamics and turbulence via pseudospectral and contour dynamics/surgery codes; 3D vortex tube interactions, reconnection, intermittency and turbulence via pseudospectral and Biot-Savart codes.