Andrea Brambilla1

Øyvind Andreassen2,3

Helwig Hauser1

Integrated Multi-aspect Visualization of 3D Fluid Flows

1 University of Bergen, Norway2 Norwegian Defence Research Establishment, Norway3 University Graduate Center at Kjeller, Norway

CFD Simulations

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Velocity

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Flow aspects

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𝑺=12

(𝛻𝒖+(𝛻𝒖)𝑇 )

𝒖 (𝒙 ,𝑡 )

𝝎=𝛻×𝒖

Velocity (motion)

Rate of strain (deformation)

Vorticity (rotation)

Related work

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De Leew and van Wick ‘93

Bürger et al. ‘08

Kirby et al. ‘99

Integrated Multi-aspect Vis

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Requirements

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Visual representationConvey local informationHandle vector and tensor data

Manage visibility issuesFocus + Context visualizationExploit data coherency

GlyphColor -> magnitudeGeometry -> direction

Velocity magnitude

Vorticity magnitude

Rate of Strain magnitude

min max

min max

min max

Multiple Focus + Context

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Different flow aspects can be more or less relevant

Swirling motion in a constant laminar flow?

The relevance of an attribute can vary over the domainMultiple relevance measures

Relevance measures

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For each attribute aDefine a set of potential locations Pa Define relevancea: Pa

-> [0, 1]

ux

min max min max

1

0

rele

vanc

e

uy

0

1

rele

van

ce

Relevance measures are user defined

Relevance measures

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For each attribute aDefine a set of potential locations Pa Define relevancea: Pa

-> [0, 1]

ux

min max min max

1

0

rele

vanc

e

uy

0

1

rele

van

ce

Relevance measures are user defined

Flow feature detectors can capture physical aspects

Hunt’s Q / λ2 / Haimes and Kenwright

1

0

rele

van

ce

λ2min max

1

0

rele

van

ce

Qmin max

Coherency and Visual Redundancy

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Information can be replicated over many samples

Visualize that information only once!

Coherency measures

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A coherency measure encodes the degree of redundancy of a set of data samples

For each attribute a, coherencya: P(Pa) -> R+

Specified by the user4 measures implemented in our systemMore measures can be easily addedSimilar overall behaviour, but small differences

test dataset 2nd moment entropy c_diffv c_dotv

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

Ap

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

Ap

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

Ap

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

Ap

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

Ap

The radius of Ap is mapped to size

The relevance of p is mapped to opacity

for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Visualization strategy

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Glyph placement algorithm:

Pa

The radius of Ap is mapped to size

The relevance of p is mapped to opacity

Visualization strategy

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Glyph placement algorithm:for each attribute a .. γa = coherency threshold .. build(Pa) .. sort(Pa, relevancea) .. for p in Pa

.. .. Ap = sphere around p .. .. while coherencya(Ap) < γa .. .. .. increase radius of Ap .. .. place a glyph in p .. .. Pa = Pa - Ap

Pa

Repeat until all the points have been processed

Repeat for every attribute of interest

Integrated Multi-aspect Vis

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Integrated Multi-aspect Vis

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Integrated Multi-aspect Vis

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Parameter settings

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Relevance corresponds to user’s interest

Coherency thresholdInitially set to 10% of maximal coherency valueCan be interactively adjusted

high thresh. mid thresh. low thresh.

Final remarks

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Our visualization strategy Presents multiple flow aspects simultaneouslyHandles visibility issues through smart placementCan be easily extended

Future work Streamlets as a new representationCoherency measure based on tensor invariantsAdapt the strategy to integral curvesExtension to time-dependent datasets

Thanks for your attention!

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Square Cylinder

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Flow in a Box

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Flow in a Box (pruned)

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Andrea Brambilla1

Øyvind Andreassen2,3

Helwig Hauser1

Integrated Multi-aspect Visualization of 3D Fluid Flows

1 University of Bergen, Norway2 Norwegian Defence Research Establishment, Norway3 University Graduate Center at Kjeller, Norway

Exhaust Manifold

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Exhaust Manifold (pruned)

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Thanks for your attention!

Brambilla et al.

Attributes of interest

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Velocity vector field

Rate of strain tensor

Vorticity tensor

Vorticity vector

𝐷𝜔 𝑖

𝐷𝑡=𝑆 𝑖𝑗𝜔 𝑗+ν

𝜕2𝜔𝑖

𝜕 𝑥𝑘𝜕 𝑥𝑘

𝑆 𝑖𝑗=12 ( 𝜕𝑢𝑖

𝜕 𝑥 𝑗

+𝜕𝑢 𝑗

𝜕 𝑥 𝑖)

𝑢𝑖 (𝑥 𝑗 , 𝑡 )

Ω𝑖𝑗=12 ( 𝜕𝑢𝑖

𝜕𝑥 𝑗

−𝜕𝑢 𝑗

𝜕 𝑥𝑖 )𝜔 𝑖𝑗=−𝜀𝑖𝑗𝑘Ω 𝑗𝑘

Vorticity transport equation

Performance

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PerformanceRelevance is pre-cumputedCoherency computation depends on

Dataset size and number of relevant pointsActual data coherencyExhaust Manifold (133x81x31) -> 0.128 sec (2.8GHz CPU)

Bottleneck is the geometry generationExhaust Manifold -> 0.470 sec / 1.037 sec (depth sort)But GPU implementation feasible!

Streamline-based Pruning

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Streamline-based Pruning

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