Visualization of Advection‐Diffusion in Unsteady Fluid Flow

Abstract

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.

Feature Driven Combination of Animated Vector Field Visualizations

“…Image‐based or texture‐based techniques generate patterns that are locally aligned with the flow field and have a high spatial frequency orthogonally to the field, thus encode well the flow direction [CL93]. Generating time‐dependent patterns by injecting and advecting noise or dye conveys next the flow speed and orientation, and can be efficiently implemented on the GPU using textures or shaders [MB95, vW02, vW03, LJH03, TvW03, LTH08, KSW∗12]. Flow can also be visualized using motion maps that generate cyclical variable‐speed animated textures [JL97, LJL04] or streamlines [JL00].…”

Generative Data Models for Validation and Evaluation of Visualization Techniques

“…For instance, rotational flow can be used to demonstrate visual artifacts in dye advection [58,71]. LCS can be investigated with an analytical model of a double-gyre flow, whose parameters allow for both steady and unsteady flow [107].…”

Vector Field Visualization of Advective‐Diffusive Flows

“…Advective‐diffusive flow has been visualized using direct volumetric visualizations of dye‐advection [KSW*12]. Topological features of advective‐diffusive flows have been examined, however, the advection‐diffusion equation has only been solved in form of a secondary simulation step on top of a purely advective flow [SKE14].…”

“…The most important approaches are volume rendering of concentration fields [EHK*06], vector field visualization of advection by means of line integral convolution [CL93], by tracing integral lines, and also by flow based surfaces [MLP*10]. However, so far mainly advective flows have been investigated while the complex flow of concentrations inside fluids, which additionally depends on diffusive flux, has not been considered in the context of integral line visualizations but only in direct volume rendering [KSW*12] and visualization of topological features [SKE14] of dye‐advection. Concentrations in the fluid have an impact on important physical quantities like surface tension, which, e.g., leads to the effect of Marangoni convection.…”