Numerical Flow Visualization: Vista and Expedition

Abstract

Numerical flow visualization resorts to data processing, feature extraction, geometric construction, image synthesis, graphical display, and scene manipulation to enable intuitive insightful interactive analysis of tangential directions of movement embedded in a velocity vector field. This paper presents some advances in numerical flow visualization over the past three decades, with emphasis on geometry-based and texture-based methods. Also introduced in this context is our own research for representing, depicting, and exploring flow data. Not intended for an exhaustive survey of the literature, our discussions revolve around streamline integration, interactive streamline placement, automatic streamline placement (including evenly spaced layout of streamlines), streamline clustering, time-dependent flow lines (e.g., pathlines), flow texture synthesis (e.g., line integral convolution), feature mining (e.g., flow topology), and parallel visualization. These topics address flows ranging from planar to surface and volumetric domains, from steady to unsteady cases, and from Cartesian to curvilinear and unstructured grids. This scope allows us to examine a variety of approaches in the working mechanism, numerical accuracy, representation effectiveness, visual quality, and computational performance so as to show the respective advantages and disadvantages. The findings may help visualization researchers pinpoint main long-lasting challenges, visualization developers identify practically applicable techniques, and domain scientists perceive important promising advances in numerical flow visualization.