Declustering in a granular gas as a finite-size effect.

The existence of dense clusters has been shown to be a transient phenomenon for realistic models of granular collisions, where the coefficient of restitution depends on the impact velocity. We report direct numerical simulations that elucidate the conditions for the disappearance of structures. We find that upon cluster formation the granular temperature and the convective kinetic energy couple and both follow Haff's law. Furthermore, we show that clusters will eventually dissolve in all finite-size systems. We find the strong power law t'∝L(12) for the dependency of the declustering time on system size. Our results imply that only in systems close to the initial critical system size both clustering and declustering transitions are observable.

Comparative visual analysis of Lagrangian transport in CFD ensembles.

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 behavior. 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.

IRIS: illustrative rendering for integral surfaces.

Integral surfaces are ideal tools to illustrate vector fields and fluid flow structures. However, these surfaces can be visually complex and exhibit difficult geometric properties, owing to strong stretching, shearing and folding of the flow from which they are derived. Many techniques for non-photorealistic rendering have been presented previously. It is, however, unclear how these techniques can be applied to integral surfaces. In this paper, we examine how transparency and texturing techniques can be used with integral surfaces to convey both shape and directional information. We present a rendering pipeline that combines these techniques aimed at faithfully and accurately representing integral surfaces while improving visualization insight. The presented pipeline is implemented directly on the GPU, providing real-time interaction for all rendering modes, and does not require expensive preprocessing of integral surfaces after computation.