Online Submission ID: 1182

Visual Analytics of Flow Features on Unstructured GridsCategory: System

Fig. 1. Idntifications of multiple shocks from the 173rd time step of the Missile dataset.

Abstract—Volume visualization and illustration techniques have proven to be effective in enhancing the depiction of scientific data.However, analysis is an essential component of visual exploration and discovery. Consequently, visualization and analysis are bestperformed within an integrated visual analytics environment. Moreover, the exploration and analysis tasks for complex, large-scaledata need to support operations and exploration on features, their spatial and numerical properties, and not simply visualization ofmassive raw data. In this paper, we introduce a novel visual analytics system for representing, discovering, analyzing, and under-standing flow features of multivariate, non-uniformly sampled datasets. Our system allows the user to visually explore and numericallyanalyze complex flow behaviors by means of a combination of feature-based transfer functions, statistical and numerical computation,and interactive illustration and photographic motifs. Spatial explorations on flow features are enabled by means of a set of struc-ture enhancement techniques in the context of unstructured grids, including Schlieren photography, shadowgraphy, silhouettes andcontour rendering. Meanwhile, statistical and numerical computation on flow properties and features (e.g., density discontinuities,directional derivatives, Mach number, vorticity and helicity) enable global quantitative analysis of flow behavior. The user is engagedin an interactive visual analytics loop with a set of visualization and illustration motifs, such as flow feature-based transfer functions,focus+context viewing, and cutaway motifs. Three critical flow characteristics, namely, vortices, flow feature separation, and shockwaves can be identified, numerically validated and visualized with our system in an easy-to-use, effective manner.

Index Terms—Flow Features, Visual Analytics, Illustrative Visualization, Multiple Shock Identification, Unstructured Grids

1 MOTIVATION

Computational fluid dynamics simulations are rapidly increasing inboth capability and scale, leading to a massive increase in the amountof data that must be processed and analyzed. The maturation of tech-nology has led science to a point where it is no longer sufficient tocompute these simulations to prove that they can be done. Rather, sci-entists are computing simulations to solve problems of significant so-cietal relevance (e.g., weather forecasting, aircraft design and safety,and artificial heart design). With the overwhelming amount of dataand potential information, it is no longer sufficient to provide analysistools that operate in ordered sequence. An integrated analytics envi-ronment is needed to combine visualizations, interactive navigation,comparative operators, and querying capabilities.

Presented in this paper is a visual flow analytics system thatal-lows computational fluid dynamics researchers to discover,describe,investigate, and predict flow behaviors with integrated analysis and in-teractive visualization tools. Our integrated environment helps flowresearchers answer questions that arise from the exploration of newconcepts, theories, and calculations. This visual analytics frameworkis designed for flow feature exploration and analysis, and builds uponthe latest visualization, illustration, and flow feature methods. Thiswork provides the following contributions:

• An effective scheme for simultaneously performing interactivespatial, structural, and numerical analysis in an integrated envi-ronment

• A user interface that enables dual domain interactions andstresses feature analysis

• A set of visualization techniques that operate explicitly on un-structured grids, including Schlieren, shadowgraphy, silhouette

and contour rendering• A set of numerical and statistical analysis tools that provide the

user insight into the defined features of the flow datasets

Figure 2 shows an overview of our visual flow analytics sys-tem. Our integrated framework reduces visual clutter whileprovidingglobal statistics and visualizations with the ability to investigate local-ized features and interesting patterns. Our visual analytics frameworkis designed to enable the efficient identification, visualization, and nu-merical validation of critical flow characteristics such asshock wavesand vortices.

We briefly summarize relevant work in Section 2 and present ourvisual analytics environment that combines illustrative motifs and fea-ture exploration toolkits in Section 3. Section 4 and Section 5 explainflow feature calculation and our extended illustrative techniques forfeature enhancement on unstructured grids. We further demostrate thedifferentiation of shock wave using our system in Section 6.Discus-sions and conclusions are presented in Section 7 and Section8.

2 RELATED WORK

2.1 Visual Analytics Systems

The need to visually analyze scientific simulations drives the devel-opment of visual analytics systems. For example, workflow sys-tems [3, 23] provide an effective visual reasoning module togain feed-back from the simulations and accelerate the workflow. Visualizationsystems [1, 8] provide general purpose visual analysis abilities on sci-entific data. The systems focusing on CFD data [2, 6] integrate mul-tiple views to assist the data exploration. However, features are not

1

Illustrative Motifs

1D/2D

Transfer function

Illustrative Feature

Enhancement

Photography

Inspired Techniques

Illustrative Feature

Feature-based

Transfer function

Statistical and Numerical

ComputationsComputations

Data

Preprocessing

Flow Feature

Statistics

Quantative

Measurement

Flow Feature

Discrete Differential

Operations

Spatial and Structural

Visualization

Focus+Context

Exploration

Cut-away

Illustration

Visual Analysis

Feature Separation

Vortex Identification

Shock Wave

Classification

iques Mea

cturaalll

nVisu

Dual domain interaction

Fig. 2. Overview of the visual analytics for flow features.

always detected due to the limitations of their rendering and analysisabilities.

Compared with previous systems that seek to combine analysis intothe visual exploration environment, our system offers moreflexibilityin both the numerical analysis and feature enhancement. With our sys-tem, multi-dimensional transfer functions can be easily designed basedon the informative characteristic of the underlying unstructured grids.In addition, our novel illustrative and photography inspired renderingsfor unstructured grid datasets help scientists to effectively visualizefeatures.

2.2 Flow Visualization and Feature Detection

Researchers have developed many techniques for representing flowdynamics with expressive glyphs (e.g., arrow plots, streamlets, andstreamlines [27]). These methods directly map the flow into apoint-based visual representation and have proven to be very useful for in-vestigating 2D and simple 3D flows. Particle traces (e.g., pathlines,streamlines, streaklines, and timelines [35, 36]) can be used to providea sparse representation of flow dynamics. By representing the struc-tures induced from particle tracing with a dense coverage, the instan-taneous structure of the flow and its temporal evolution can be clearlyvisualized (e.g., LIC [28] and texture advection [18, 37, 40]).

Feature-based flow visualization computes an abstractive represen-tation by filtering the data based on regions of interest. Common fluidflow features include vortices, shock waves, separation andattachmentlines, recirculation zones, and boundary layers. These techniques canbe classified by their approach: image processing, topological analysisand physical characterization of the flow [24]. Topology-based meth-ods [27] are used to find interesting critical points [26]. Specific meth-ods are used to find other flow features such as vortices [10, 12, 14, 25],shock waves [17, 20] and feature separation and attachment [13].Shock waves and separation and attachment lines typically requirespecifically designed extraction techniques that are basedon physi-cal or properties of the flow. Hierarchical methods based on clusteringhave been used for vector simplification and to provide spatial infor-mation [35].

2.3 Volume Rendering and Illustration on UnstructuredGrids

Previous work on visualizing unstructured grids can be roughly di-vided into two classes, ray casting and cell projection. By decom-posing the projected shape of a tetrahedron into multiple triangles,

the projected tetrahedra algorithm [29] is suitable for sparse datasetsand easily accelerated with graphics hardware [16]. StraightforwardGPU implementations of ray casting [22, 38] and cell projection [39]have achieved good speedup through parallelism. Other GPU-basedapproaches either reduce the rendering artifacts [16], or improve theperformance by employing optimized data structures [4, 5].

Illustrative visualization techniques enhance the structural percep-tion of datasets through the amplification of features and the additionof artistic effects. Typical volume illustration algorithms [7] work forregular volume data and are limited to moderate data sizes. Inspiredby the art and photography used in experimental flow visualization, il-lustrative visualization of flow dynamics has attracted theattention ofmany researchers [11, 15, 31, 33]. Although the work in [32] extendsvolume illustration to irregular volume data, it does not incorporatemany advanced flow features.

GPU-based Projected Tetrahedra (PT) rendering engine [30]en-ables two-dimensional transfer function design and rendering on tetra-hedral grids. We extend this work with illustrative visualization tech-niques for flow feature enhancements.

3 VISUAL ANALYTICS FOR FLOW FEATURES

Our system tightly integrates a dual domain, interactive visual analyt-ics user interface with a number of components: 1) spatial and struc-tural visualization, 2) illustrative exploration, and 3) statistical and nu-merical computations. The integrated use of a sequence of interac-tive motifs such as multivariate transfer functions, feature statistics,focus+context and cutaway viewing guides the user’s attentive focuswhile de-emphasizing distracting details. This section gives a descrip-tion of each component of the visual analytics system and a demon-stration of the system’s feature detection capabilities.

3.1 Dual Domain User Interface

We have developed a novel user interface (Figure 3) that adopts a dualdomain interaction mode, allowing the user to simultaneously performboth statistical and visual exploration and validation.

The left side of the user interface is designed to accomplishthe visual exploration tasks using both two-dimensional and three-dimensional displays. The top left window provides basic two-dimensional explorations by means of cutaway viewing widgets.Interactive three-dimensional spatial and structural explorations areshown in the bottom left window. Supported visualization modes in-clude standard volume rendering, feature-oriented volumeillustration,photography-inspired visualization and focus+context exploration.

Statistical exploration and validation are controlled anddisplayedin three subwindows and one panel on the right side of the userinter-face (Figure 3). Different flow properties including density, velocity,helicity, divergence and directional derivatives are plotted and manip-ulated in each window with associated numerical labels. Other com-putational values include the normal Mach number, pressure, and thedistance of cells with a given value to the geometry. The histogram ofeach property or value is displayed allowing the user to select subre-gions of interest. This selected or filtered subregion is then visualizedwith different colors and opacities using the two-dimensional trans-fer function shown in the bottom right display window. The user canselect values for thex andy axes and further refine the display by in-teractively manipulating the multivariate transfer function.

For scientists and engineers, our dual domain user interface pro-vides substantial user flexibility and efficiency. Visual analysis, ex-ploration and validation provide a global view while allowing the userto navigate and zoom on demand. The integration of both the interac-tively controlled visual display and the statistical viewsof the variablesof interest provides the user with a complete analysis environment.This allows the scientist to better design and evaluate the numericalproperties of the flow more thoroughly. Additionally, this allows theuser to achieve more meaningful visual effects (Section 5) by leverag-ing the explored statistical and numerical information.

The entire interaction is coupled between the two domains inaneasy-to-use and effective manner. The dual domain user interface pro-vides the best combination of speed and accuracy. As the exploration

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Online Submission ID: 1182

2D Cut-away View

3D Rendering Window Transfer Func�on

Edi�ng Window

Control Panel

Constraint Filtering Windows

Sta�s�cal Query Window

Fig. 3. A screen shot of the user interface for the visual flow analytics system.

advances, the attention of the user is progressively directed to the mostprominent regions or flow features that answer their questions. Thisenables the user to obtain accurate analysis results more efficiently.Note that numerical values can be validated in both domains at anytime, and are used for further discovery and decision making.

Figure 3 illustrates the use of the visual analytics environment toanalyze the Delta Wing dataset. To investigate vortices in the flow,the user first employs the two-dimensional cutaway widget showingthe vorticity. This allows the user to get a localized view ofthe flowover the body and in the far field. From there, the user can choose tofurther investigate both the existence and location of the vortices andtheir causality. The constraint filtering windows allow theuser to get aglobal view of the distributions of the norm of the density gradient andthe cell distance to the body. This information is used to filter the dataand feeds into the two-dimensional transfer function basedon the vor-ticity and density. The user can then interactively design and refine thismultivariate transfer function based on the visual output in the transferfunction editing window. Statistical information regarding the transferfunction defined cells is displayed in the statistical querywindow. Avolume rendering of the formation of the vortex tube is shownin thethree-dimensional visual exploration window at the bottomleft.

3.2 Statistical and numerical analysis

Our system automatically derives new flow fields based on the loadedraw data fields. These fields include basic flow properties, vector fieldsand shock wave properties. The complete list of flow fields along withtheir derivation equations are shown in Table 1. The distribution foreach property can be represented with a one-dimensional curve anddrawn within the labeled physical coordinates, as demonstrated in theconstraint filtering window in Figure 3. The correlation between theselected properties is illustrated in the bottom right window and is thebasis for the design of the multivariate transfer function.

Statistical information regarding a single field can be easily ob-tained through our statistical query interface. The extremes, mean,standard deviation and other statistical properties (see Table 2 for acomplete list) are computed upon user’s requests based on the datadistribution of the cells that are selected by the designed transfer func-

tions. The statistical query window showing the data distribution andstatistical information is shown in Figure 3.

The statistics and numerical computations on the flow propertiesare used to detect features by converting each user-defined data rangeinto a statistical filter and applying this filter as a two-dimensionaltransfer function. As a result, the selection of statistical and numericalanalysis is immediately visualized in the visual exploration windows,greatly improving the exploration performance. Meanwhile, the sta-tistical information can be queried, giving more insight into the datadistribution. Moreover, if there are any abnormalities detected in thevisualization results, the user can quickly investigate the problem byquerying the available statistics and numerical computations.

Table 1. Flow data fields and evaluation equations

Data Field EquationDensity gVelocity ~h(v)Energy ePressure pTemperature TDensity Gradient ∇gDensity Gradient Magnitude ‖∇g‖Laplacian ∆gNormal Mach Number M

First Directional Derivative δ1g =~h‖~h‖

·∇g

Second Directional Derivative δ2g =~h‖~h‖

·∇(~h‖~h‖

·∇g)

Weighted Density Gradient ‖∇g‖−Σv j ω j‖∇v j g‖

Divergence div(~h)

Curl curl(~h)Helicity HDistance to Body dist(·)

We demonstrate the capability for feature separation with the ON-

3

Table 2. Statistical Properties for a single data field

Property EquationNumber of Cells nTotal Volume VExtreme minimum(·), maximum(·)Mean gMedian gStandard Deviation σ

ERA M6 Wing dataset shown in Figure 4. Using traditional two-dimensional transfer functions, the flow features are difficult to dif-ferentiate visually (Figure 4 (a)). We refine the investigation by lim-iting the visualization to values that fall within a selected value rangeof cell distance to the M6 wing, yielding Figure 4 (b). We could alsorefine the result by limiting the Mach number to get Figure 4 (c). Fi-nally, a shock wave is fully detected and visualized (Figure4 (d)) byemploying both the filters for the distance and the Mach number.

(a) (b)

(c) (d)

Fig. 4. Feature separation by employing a sequence of statistical filtersto the ONERA M6 Wing dataset. (a) Standard transfer function basedrendering; (b-d) Adding additional data filters clearly isolates the regionof interest. The transfer functions are shown in the top left corner ofeach figure.

3.3 Illustrative and Photographic Motifs for Flow FeatureExploration

For efficient spatial navigation, we employ a focus+contextinteractionmode to direct the user’s attention to the most important regions. Theuser is allowed to move a sphere-based motif to locate and resize thefocus region. Different illustration styles can be appliedto the focusand context regions, as shown in Figure 5 (a).

Our system provides a cutaway viewing motif that allows the userto flexibly explore the data along an arbitrary cutting plane. By pro-gressively changing the position of the cutting plane and displaying thevalues on that plane, the scientists can easily gain an overview of the

flow features without any visual clutter. Figure 5 (b-d) shows the den-sity and Mach number with the cutaway traversal mode. Note the colorpattern difference between Figure 5 (c) and (d) that helps the scientiststo understand the Mach number distribution as well as investigate thelocation of shock waves.

This mode allows the users to not only simulate photographicflowvisualization techniques in the entire space, but also mimic their ef-fects within any cutting plane, as shown in Figure 9 (a).

(a) (b)

(c) (d)

Fig. 5. Interactive motifs demonstrated with the Missile dataset. (a)Focus+context exploration; (b) A cutaway view of the density distribu-tion; (c-d) Two cutaway views of the Mach number on different clippingplanes. In (a), a geometric model for the aircraft is mixed in the scene.For (b-d), the cutting plane positions are illustrated as small snapshots.

4 FLOW FEATURE CALCULATION

CFD simulations produce multiple variables at each node. However,these variables alone are not sufficient for feature discovery and needto be expanded. Our system derives new flow fields based on the rawvariables. The complete list of fields is listed in Table 1 along withtheir mathematical equations. Moreover, per-vertex gradient and dis-crete vector fields are computed on user-selected fields for feature en-hancement.

(a) (b)

Fig. 6. Rendering the Blunt Fin data with (a) per-tetrahedra and (b)per-vertex gradient computation modes.

4

Online Submission ID: 1182

4.1 Per-Vertex Gradient Computation

In most previous work, a constant gradient for each tetrahedron isused for lighting [16, 38]. Although this scheme is fast, it yieldsunsatisfactory results similar to flat-shading in surface rendering thatemploys a constant normal for every triangle. To compute a per-vertex gradient, there are three categories of methods, namely, gra-dient average, Green-Gauss, and linear regression methods. Our sys-tem adopts the gradient average method to achieve the balance be-tween the performance and quality. It computes the gradientof avertex vi as the weighted average of the gradient of its neighboringtetrahedra:∇vi g = ∑t j∈Nt(vi) ω j∇t j g, whereNt(vi) denotes the set of1-ring neighboring tetrahedra ofvi and ω j denotes the weight. Fig-ure 6 depicts the results from per-tetrahedra [16] and per-vertex gradi-ent computations. Visually better results are achieved using per-vertexvalues than per-tetrahedra values.

4.2 Discrete Differential Operators on Tetrahedral Meshes

For a discrete vector field~h(v) defined onS, we can compile itsdiscrete divergence at vertexvi as div(~h(vi)) := ∑t j∈Nt(vi)(

~h(t j) ·

∇φi∣∣t j )Gt j , where Gt j is the volume of the tetrahedront j. Like-

wise, we can define the discrete curl operator: curl(~h(vi)) :=

∑t j∈Nt(vi)(~h(t j)×∇φi

∣∣t j )Gt j , where× denotes the vector cross oper-

ation [34]. Note that~h can be either an arbitrary vector field definedon S or ∇g that is derived from the discrete potential fieldg. In thelatter case, we can further derive a discrete Laplacian operator for g:∆g := div(∇g) and compute the helicity that represents the curl in thedirection of the velocity field: curl(~h) ·~h.

These discrete differential operations are physically meaningful andbenefit the visual analysis of the flow dynamics: the divergence opera-tor sums the flux of the vector field through the one-ring neighborhoodaround a vertex, and the curl operator sums the vorticity of the compo-nent of the input vector field tangent to each face opposite toa vertex.We apply them to the input flow and construct a set of two-dimensionaltransfer functions by employing|∇g|, div(~h), |curl(~h)|, ∆g as the sec-ond dimensional parameters respectively, as shown in Figure 7.

(a) (b)

(c) (d)

Fig. 7. Visualizing the NASA X38 data with different differential-basedtransfer functions: (a) (g,∇g), (b) (g,div (~h)), (c) (g,|curl(~h)|), (d) (g, ∆g).The geometric body of the X38 is rendered in gray.

5 FLOW FEATURE ENHANCEMENT

The human visual system is great at the identification of oriented sur-face structures in uncluttered three-dimensional spaces,but is lessadept at understanding data that fills space continuously. To succinctlyidentify and characterize structural information, we extend the illustra-tion and photography inspired visualization of flows [33] tounstruc-tured grids.

5.1 Illustration of Oriented StructuresOur system supports the following illustrative effects (Figure 8) forinvestigating the flow features with oriented structures:Boundary Enhancement: We assume that the gradient changes lin-early along a ray segment with lengthl. Given the gradient vectors∇g f and∇gb

1 and opacitiesτ f andτb of the entry and exit points, wemodulate their opacities to beτ f |∇g f |

p andτb|∇gb|p wherep is the

enhancement coefficient. The opacity of this ray segment becomes:

αi = 1−exp(−l2(τ f |∇g f |

p + τb|∇gb|p)) (1)

It can be further extended to depict boundaries defined by other vec-tor field operators described in Section 4.2, yielding different effectssuch as gradient magnitude isolines, curvature-based illustration andcurl structure. For instance, we can enhance regions with strong diver-gence:

αi = 1−exp(−l2(τ f |div(~h) f |

p + τb|div(~h)b|p)) (2)

View-dependent Enhancement: Standard silhouette enhancement isfulfilled by incorporating the viewing vector~V in the ray segmentopacity computation:

αi = 1−exp(−l2(τ f (1−|∇g f ·~V |)p + τb(1−|∇gb ·~V |)p)) (3)

By replacing ∇g with other differential operators, different view-dependent effects can be achieved.Contour Volume Effects: Similar to [33], we simulate the bandingeffects by modulating the opacity with asine function:

αi = 1−exp(−l2(|

1+sin(τ f ·π ·m)

2|p + |

1+sin(τb ·π ·m)

2|p)) (4)

wherem is an adjustable phase constant.

5.2 Photography inspired techniquesSchlieren and shadowgraphy are two photographic flow techniquesthat use one-dimensional gradient variations to reduce thevisual clut-ter of the flow. These techniques are incorporated into our systemfor unstructured grid feature enhancements using a similaralgorithmto those that operate only on rectilinear grids [33]. We compute thedisplacement vector~ε and luminance mapL in a tetrahedron by accu-mulating the displacement’s projections on thexy-plane and the lumi-nance distribution along the segment between the entry and exit points:

~ε =1−exp(−l2((

∂g∂x

) f +(∂g∂x

)b)

L =1−exp(−l2((

∂ 2g

∂x2 +∂ 2g

∂y2 ) f +(∂ 2g

∂x2 +∂ 2g

∂y2 )b) (5)

Thereafter, two Schlieren effects with different cutoff methods can besimulated with:

Knife-angle: I = s (1+~ε·~k)2

Circular: I = s |~ε| (6)

where~k denotes the vector that is normal to the knife edge. The shad-owgraphy effect is computed analogously:I = s(1+L)/2.

Figure 9 illustrates four photography-inspired results for the NASAX38 dataset.

1We usef andb to denote the front and back points of a ray segment.

5

(a) (b)

(c) (d)

Fig. 8. Illustrating oriented structures of the Delta Wing dataset with:(a) a conventional transfer function; (b) the gradient based boundaryenhancement; (c) the view-dependant gradient enhancement; (d) theview-dependant curl enhancement. A geometric model for the wing isrendered in grey in the scene.

6 SHOCK WAVE VISUALIZATION AND CLASSIFICATION

Previously, shock waves have been visualized using thresholding of avariety of numerical calculations [9, 17, 19, 20, 21]. Ma, etal. [20]present three approaches. The first one computes the normal Mach-

numberM in the direction of the density gradient:M =||h||

a , where

h denotes the projection of the flow velocity onto the density gradi-ent anda is the speed of sound. The points where the normal Mach-number equals 1.0 form the shock. The second method computesthezero-level iso-surface of the second directional derivative of the den-sity g of the flow byδ2g =

~h||~h||

·∇(~h||~h||

·g). The parts of the iso-surface

where the normal Mach-number is close to 1.0 are in a shock region.The third method compares the weighted average of the norm ofthedensity gradients at the vertices neighboring certain vertex vi and the

(b)

(d)

(a)

(c)

Fig. 9. Photography-inspired illustrations for the NASA X38 dataset. (a)A cutaway-enabled 2D schlieren rendering; (b) A Schlieren effect with60 degree knife-edge cutoff; (c) A Schlieren effect with circular cutoff;(d) A shadowgraphy effect.

norm of the density gradient invi: ||∇vi g|| −∑v j∈Nv(vi) ω j||∇v j g||. Ifthe difference is positive,vi is assumed to be in the vicinity of a shock.Despite their attractiveness, all these methods can only roughly iden-tify shock regions, but do not provide a means of detecting the exactshock regions and differentiating multiple shocks.

With our visual analytics system, the detection and visualizationof shock waves can be easily accomplished by integrating thenormalMach number, gradient norm or directional derivatives intothe two-dimensional transfer function. The visualization of shockwaves fortwo time steps of the Missile dataset are shown in Figure 10.

(a) (b)

Fig. 10. The shock waves for the Missile dataset at the 10th frame (a)and 173rd frame (b).

One distinctive feature of our system is that multiple shockwavescan be further differentiated. Typically, the norm of the density gradi-ent, the density or the distance to the body are used as the statisticalproperties used in the constraint filtering windows. The twovariablesused in the transfer function design window can be the norms of thefirst and second directional derivatives, or the normal Machnumber.The user can choose two intervals from the two histograms andapplythe resulting filters to the two-dimensional transfer function to differ-entiate multiple shock waves into primary and secondary shocks.

An example of detecting and differentiating multiple shocks on theMissile dataset is shown in Figure 11. When loading the data,theuser can choose an initial view that is shown in the 2D cut-away viewwindow of the system. In this figure, the user has chosen to display aSchlieren view to visually locate and highlight possible shock regions.The user can then choose data variables to further investigate the datadistributions from their histogram plots. For the Missile dataset, den-sity gradient norm and density are chosen.The user then applies a re-gion selection by choosing a rectangular region on each of the datadistributions. The selected values are reflected in the two-dimensionaltransfer function. The first and second directional derivatives are cho-sen to construct the multivariate transfer function, and the user refinesthe display by selecting values that have a second directional derivativenear zero and a positive first directional derivative. The combinationof these techniques and the coupling of interactive visualization allowsthe user to rapidly refine the visualization to show only the shock re-gions. The ability to use different region selections helpsthe user tosee the differentiation of primary and secondary shocks in Figure 11.

7 RESULTS

We have implemented and tested our system on a PC with a P4 3.0GHZ CPU, 4.0GB RAM and a Nvidia Quadro 5600 video card. Inaddition to the rich set of rendering effects described in this paper, oursystem provides point- and wireframe- based views as well as2D cut-away views to allow the users to quickly locate the regions ofinterest.

Our test datasets include five three-dimensional computational sim-ulations. The Blunt Fin dataset is a numerical simulation oftheReynolds-averaged Navier-Stokes equations for supersonic flow overa blunt fin mounted on a flat plate [9]. The ONERA M6 Wing datawas tested in a wind tunnel at transonic Mach numbers (0.7, 0.84,0.88, 0.92) and various angles-of-attack up to 6 degrees. The NASA

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Online Submission ID: 1182

(a) (b)

(c) (d)

Fig. 11. The differentiation of the primary and secondary shock wavesfor the Missile dataset at the (a,b) 10th frame and (c,d) 173rd frame. Foreach frame, a Schlieren view is shown. Note that, the 3D shock wavesagree with the 2D Schlieren views.

X38 dataset records a single time step of the crew return vehicle dur-ing reentry into the atmosphere at a 30 degree angle of attack. TheDelta Wing dataset is designed to investigate the causes of the strongnonlinearities (critical states) occurring in the forces and moments of asharp-edged 65-degree delta wing at sideslip. The Missile dataset sim-ulates booster separation of a rocket and has 361 frames withthirteenvariables including density, Mach number, and momentum. The gridis a mixed element unstructured grid containing tetrahedra, hexahedra,pyramids and prisms. We unify all primitives into tetrahedra prior tovisualization. One half of the Missile dataset is used for visualiza-tion. Note that, in most of the visualizations we integrate the geomet-ric body generated with a marching tetrahedra algorithm to provide aspatial frame of reference.

The results and comparisons for five datasets have been showninthe paper. Figure 3, 4, 10, and 11, respectively, demonstrate three ap-plications for visualizing vortices, flow feature separation, and shockwaves and their differentiation. Figure 12 displays the shock struc-tures and the spinning motion around a finned missile as it traversesthrough space. The shock structure is clearly illustrated in Figure 12(a). The missile is released at high velocity and the presence of thefins causes a spinning motion. As the missile begins to decelerate,secondary and tertiary shocks will form. Because of this relationshipbetween spin and velocity, it is able to visually inspect therelation-ship between helicity and the shock structures over time. Figure 12 (b,c) display both the vorticity and helicity and allow us to compare theseparated structures on a single time step.

8 CONCLUSION

With the dramatic increase in computational power available to thenational simulation community, the capability and capacity for com-puting ever more complex fluid dynamics simulations is growing. Thissurge of growth has been both an extraordinary breakthroughfor thecomputational scientists and a challenge for those analyzing the re-

(a)

(c) (d)

(b)

Fig. 12. Visualization of a Finned Missile spinning through space. (a)The contour volume effect around the body of the Missile dataset clearlyshows the shock that occurs around the nose and stretches over thefins; (b) Visualization of the vortex shows the spinning motion aroundthe front fin of the Missile dataset; (c) Visualizing high helicity refines thedisplay of the spinning motion; (d) Visualization of the feature separationof the X38 dataset shows the bow shock as it emanates over the body.

sults. The tremendous growth in computational capability naturallygives rise to ever increasing data set sizes, and the traditional model ofanalyzing results from a single image or movie is now outdated. Inte-grated interactive visualization and analysis plays an essential role inexploring current and next generation flow simulations and closing thisgap. Integrating data mining, data analysis, visualization and featuredetection into a unified interface provides a very powerful tool for in-teractively discovering and verifying relevant information from thesemassive simulations. Relevant features can be extracted and classi-fied, allowing the user to rapidly explore new models by understandingsalient features in the flow.

This system was designed in collaboration with computational fluiddynamicists and is a result of balancing their visualization needs withanalysis requirements. We have described our visual flow analyticssystem that enables spatial and numerical analysis throughillustra-tive visualization and statistical techniques. This system allows a userto easily identify flow features while interactively obtaining informa-tive feedback. We demonstrate the robustness and efficiencyof oursystem with three challenging flow visualization tasks including flowfeature separation, vortices, and shock wave detection andclassifica-tion. We have also demonstrated our system’s novel ability to detectand differentiate between multiple shocks for further analysis, solvingan important problem in flow analysis. We strongly believe that thissystem will significantly aid in the development of CFD simulationsand in their subsequent analysis, particularly at very large scale. Wehave extended a set of existing structure enhancement techniques inthe context of unstructured grids to better depict the flow features. Inthe future, we would like to investigate the dynamic behaviors of flowfeatures within a sequence of datasets.

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