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Visualization of Advection-Diffusion in Unsteady Fluid Flow

This web page contains additional material accompanying the Eurovis 2012 paper "Visualization of Advection-Diffusion in Unsteady Fluid Flow" by Grzegorz Karch, Filip Sadlo, Daniel Weiskopf, Claus-Dieter Munz, and Thomas Ertl.


Advection has been the standard transport mechanism in flow visualization. Diffusion, in contrast, has not been considered important in visual flow field analysis so far, although it is inherent to many physical processes. We present a novel technique that allows for interactive 3D visualization of both advection and diffusion in unsteady fluid flow. We extend texture-based flow visualization, which is advection-oriented, by diffusion. Our finite volume approach based on WENO (weighted essentially non-oscillatory) reconstruction is well parallelizable and features low numerical diffusion at interactive rates. Our scheme contributes to three different applications: (a) high-quality dye advection at low numerical diffusion, (b) physically-based dye advection accounting for diffusivity of virtual media, and (c) visualization of advection-diffusion fluxes in physical media where the velocity field is accompanied by a concentration field. Interactive rendering of the virtual dye is accomplished by ray casting. We apply our GPU implementation to CFD examples of thermal convection and evaporation phenomena.

Publication Download

A PDF version can be found here.


The following videos demonstrate the quality of our dye advection method, as well as the utility of advection-diffusion visualization.

Unsteady buoyant air flow (CFD) in a closed container heated at bottom (red plate, 75C) and cooled at the top (blue plate, 5C). Two isosurfaces, one at 38C (blue) and one at 42C (red). Advected dye (green, without diffusion model) seeded at center. Finite volume method using WENO reconstruction exhibits low numerical diffusion. Dye resolution at 244 x 122 x 244 in the figure and at 61 x 31 x 61 in the video. [MP4] [PNG]

Heating coil example. Air flow from bottom to top, dye (green) seeded at two points at lower side of coil, and isosurfaces of temperature (orange, yellow). Dye advection by advection only (left) vs. dye advection by advection-diffusion of heat (right). It is apparent that heat is repelling the dye from the coil and transporting it to the cooled walls in the left figure.
[MP4-1-advection] [MP4-2-advection-diffusion] [PNG]