Visualizing fluid flow Lnitwiice .I. Rosetthlriiiz.Office of Ntrvnl Resetrrch Eifropc'czii Office Frirc H . Post. Delfi University of' Technology

Global warming. the space shuttle. blood flow through the heart, microscale ocean phenomena. aircraft and automo- tive design. and coastal erosion protec- tion: These are just a sampling of the many critical topics that depend on liq- uid o r gaseous fluid-flow modeling for analysis. Using techniques such as finite differences. finite elements. and multidi- mensional fast Fourier transforms. these computational fluid-flow simulations typically require supercomputers o r massively parallel processors to perform the necessary calculations.

Scientific visualization. Computation- al physics algorithms produce huge amounts of numbers as output. But what's the next step? The two-dimen- sional fluid-flow simulations of the last two decades provided innumerable deni- onstrations that the standai-d graphics of

the day. contour plots. were inadequate for extracting detailed understanding. Scientists would thumb through stacks of these contour plots. one for each time step in the simulation. trying to comprc- hend the dynamics. But it just couldn't be done.

New computer graphics tools met the challenge. After data filtering and color coding of parameter values at each pix- el. animation was used to enhance per- ceptual understanding. ( A frame from such an animation graced the covei- of the National Science Foundation report. "Visualization in Scientific Computing." that gave the field of scientific (01- data) visualization i t s name.)

Two-dimensional data-visualization techniques incorporated in commercial systems now offer easy accesb even to scientists untrained in visualization. The techniques are partially extensible to

3D. and their use within the scientific community is increasing rapidly. How- ever. recent advances in supercomputer and workstation power have led to in- creased numbers of 3D simulations.

The third dimension significantly in- creases the difficulty o f data visualiza- tion. The development of 3D algorithms that make little sense in 2D and the ex- tension of 2D techniques to 3D have be- come ..hot topics'' to aid understanding of the world around and within us.

Fluid flows. Fluid flows can he charac- teriLed by diflereiit types of curves. A particle path is the path traced by a sin- gle. infinitesimally small fluid clement. A streak linc arises when particles are continuously inserted in a flow from a single fixed position over a period of time. A streamline is thc integral curve of the instantaneous velocity vector field

courtesy of Cfemens La ufactucing Technotogy,

98 COMPUTER

passing through a given point at a given time. The resulting curve is everywhere tangent to the flow direction.

All of these curves provide important clues about the underlying physics. They all coincide for steady. time-indepen- dent flows. but they can be very differ- ent in unsteady. time-dependent flows.

streamline. Just as a single particle trac- es a curve. a base curve (consisting of an infinite number of particles) traces a surface in the flow over time. Stream surfaces can improve insight into com- plex flow-field structures by providing depth and orientation cues through shading and hidden-surface elimination.

Visualization techniques. A common

The stream surface extends the

technique in fluid flow visualization is the insertion of particles into the flow to. for example. animate the particle's time-dependent position or generate streamlines or stream surfaces. Each technique illuminates different charac- teristics. and technique selection is prob- lem specific.

Older particle-rendering methods generally treated the particle as a point. Advantages accrue from treating the particle as a very small facet with an as- sociated surface normal. The facet's small sire makes shape irrelevant. but knom#ledge of the normal assists the vi- sualization pi-ocess by allowing light rc-

flection calculations. A dense cloud of these particles can have surface-like properties. Stream surfaces can be simu- lated using these "surface-particles," generated by user-defined particle sources that have geometric and time- related attributes. Figure 1 is a frame from an animation sequence of surface particles moving in a thermal flow in a T V set.

The generation of isosurfaces is useful for examining the interface between re- gions with different properties. especial- ly when transparency is used to enable viewing several isosurfaces at once. Fig- ure 2 is a frame from an animation that studied fluid injection t o displace oil f rom minute pores within the rock ma- trix of a reservoir. Animating a visual- iLation contining the water. solvent. and oil isosurfaces helped determine the best method for the oil recovery proccss.

Volume rendering. a 3D display meth- od that does not depend on constructing an object's surface, is valuable for seeing inside an object or displaying nebulous objects such a s clouds. These properties make volume rendering a natural choice for examining flow fields. However, vol- ume rendering is most suitable for visu- alizing scalar data. Thus, velocity ( a vec- tor) cannot be displayed directly. Accordingly, scalar quantities are asso- ciated with the vector data (for example. pressure and temperature) o r derived

from velocity (for example, speed and velocity magnitude). By associating opacity with the scalar value (for exam- ple. pressure) for each cell. all space is transparent unless occluded by a param- eter of interest with high opacity value.

Figure 3 shows how volume rendering can be combined with surface-rendering methods for flow visualization. The sca- lar data (the transparent nebulous spots) are calculated by dispersion of polluting substances in sea water as caused by tid- al currents. The surfaces are recon- structed from measured undersea ter- rain (bathymetry) data and rendered as polygons.

Data probing methods designed spe- cifically for 3D fluid-flow analysis help scientists extract information about spe- cific regions in a flow field. The 3D probing is straightforward: however. a glyph ( a geometrical object with infor- mation encoded in the geometry or asso- ciated attributes such as color) is used to encode information about the region near the data point. Components of the local flow field are derived and encoded onto the glyph.

Figure 4 shows a glyph whose compo- nents are derived by a decomposition of the velocity gradient tensor, calculated in a local coordinate frame, where one axis is aligned with velocity direction. This results in quantities such as the cur- vature of the streamline through the

J u n e 1993 99

probe point. convergence, shear. and he- licity (rotation component). Each of these quantities is associated with a spe- cific part of the glyph. Figure 4 shows the probing device with the geometric components representing the different flow quantities.

ized analysis and visualization tech- nique\ are developed. An example is turbulent flow. which uses statistical methods t o model random fluid mo- tions. For visualization, a turbulent mo- tion effect can be obtained using particle animation. Adding a perturbation to the smooth convective motion results in er- ratic "random walk" motions. This per- turbation is based on numerical data produced bq the turbulence model and directly reflects the random dynamics of the turbulent motions. Figure 5 shows a frame from a simulation of turbulent mixing o f fluids.

An important branch of the current work in fluid flow visualization is based

For specific flow phenomena, special-

on topological considerations. The to- pology of a vector field consists of criti- cal points where the velocity vector i s zero and of integi-al curves and surfaces connecting these critical points. Vcctor- field topology images show the field's topological characteristics without too much redundant information. The posi- tions of the critical points are found by searching the cells in the flow field. Once identified. they are classified by examining the eigenvalues of the partial derivatives of the vclocitv. The topologi- cal information then becomes the input to computer graphics rendering alpo- rithms to examine the flow field. Figurc 6 shows the topology of a 3D f low field.

Ext en si ons. The v i s u a I i z a t ion m c t h - ods for scalar and vector fields a lso have extensions to tensor fields. Another in- teresting research direction l ies in the use of virtual reality (sec "Hot Topics." Feb. 1993 Cor?~piirrr. pp. 79-83), An open research question is "what gains

result when a user is immersed within a data set. as opposed to seeing it on a screen'?" The "virtual windtunnel" re- search at the NASAiAmes Research Ccnter i s examining this question for fluid flow around objects.

Further reading T. Dclmarcelle and L. Hesselink, "Visual- [Ling Second-Order Tensor Fields with Hy- perstreamlines." l E E E CG&A. Vol. 13. N o . 4. t o appear July 1993.

F. Post and 'I. van Walsum. "Fluid Flow Vi- \ualiration." in Fociis on Scicwrific Viritnl- i:o/ion. H. Hagen. H. Mueller. and G. Niel- mi. eds.. Springer Verlag. 1993. pp. 1-40.

J . J . van Wijk. -Rendering Surface Parti- clcs." fr-oc. ViAiuilizcrrion Y2, Order No. 7897-02. IEEE CS Press, Los Alamitos. Calif.. 1'992. pp. 53-61.

Lawrence J . Rosenblum is liaison scientist at the Office of Naval Research European Office. 223 Old Marylebone Rd.. London N W l 5TH. I JK . His e-mail address is Ii-osenhlum~onreur.navy.mil.

Frits H. Post is associate professor of com- puter graphics a t Delft Iiniversity of Tech- nology. Dept. of lechnical Informatics. Julianalaan 132. 2628 BL Delft, The Neth- crlands. His e-mail address is fr i ts~:dut ica . tudelf t .nl .

Figure 5. A frame from a simulation

urtesy Henk van den Boo- lft Hydraulics, The Nether-

ualuation by Andrea Hin, rsity of Technology, The

6. Vector field topology analy- ed on determination of critical in the flow field where the ve- s zero. The flow configurations

around these critical points are then classified using the eigenvectors and eigenvalues of the matrix of first-or- der partial derivatives of the velocity field. The stream surfaces generated act as surfaces of separation in the ex- ternal flow. (Reprinted from "Visual- izing Vector Field Topology in Fluid Flows" by James Hetman and Lam- bertus Hesselink of Stanford Univer- sity, IEEE CG&A, May 1991)

C O M P U T E R