Visualizing Multivalued Data from 2D
Incompressible Flows Using Concepts
from Painting
R. M. Kirby H. Marmanis D. H. Laidlaw
Brown University
Presented by Hsin-Ji Wang & Chaoli Wang







Oil Painting of the Impressionist
Basic Fluid Mechanics Concepts
Related Work
Visualization Methodology
Example 1: Rate of Strain Tensor
Example 2: Turbulent Charge and Turbulent
Current
Summary and Conclusions
Oil Painting of the Impressionist

The multiple layers of brush stokes in these
paintings provide a natural metaphor of constructing
visualization from layers of synthetic “brush stokes”.

The works of three painters they studied
–
–
–
Gogh, Vincent van (1853-1890)
Monet, Claude-Oscar (1840-1926)
Cezanne, Paul (1839-1906)
Oil Painting of the Impressionist
Van Gogh, whose large, expressive,
discrete strokes carry meaning
both individually and collectively.
Two Cypresse (1889)
Oil Painting of the Impressionist
Monet, whose smaller stokes are
often meaningless in isolation –
the relationships among the stokes
give them meaning, far more than
in van Gogh.
Woman Seated under the Willows
Oil Painting of the Impressionist
Cezanne, who combined strokes
into cubist facets, playing with 3D
perspective and time within his
paintings more than either van
Gogh or Monet. His layering also
incorporates more atmospheric
effects. In a sense, his work shifts
from surface rendering toward
volume rendering.
The Card Players
(1890-1892)
Oil Painting of the Impressionist
Van Gogh's The Mulberry Tree (1889) illustrates the visual
shorthand that van Gogh used with his expressive stokes. Multiple
layers of stokes combine to define regions of different ground cover,
aspects of the hillside, and features of the tree. An underpainting
shows the "anatomy" of composition of the scene in broad stokes.
Oil Painting of the Impressionist




Capture the marriage between direct representation
of independent data and the overall intuitive feeling
of the data as a whole
Space: encode different information at different
scales
Time: design visualizations so that important data
features are mapped to quickly seen visual features
Choose the artists in whom you have a passionate
interest, any artist has lessons to offer to
visualization
Basic Fluid Mechanics Concepts





Vorticity
Reynolds Number
Rate of Strain Tensor
Turbulent Charge
Turbulent Current
Basic Fluid Mechanics Concepts

Vorticity
–
–
–
–
ξ=▽×u
Vorticity is primarily used to describe the rotation of
fluid.
If ▽ × u = 0 then the fluid is irrotational
else the fluid is rotational
Basic Fluid Mechanics Concepts

Reynolds Number
–
–
Reynolds number = ρVD / μ
Reynolds number is proportional to { (inertial force) /
(viscous force) } and is used in momentum, heat, and
mass transfer to account for dynamic similarity.
Basic Fluid Mechanics Concepts

Rate of Strain Tensor
–
–
The symmetric part is known as the rate of strain
tensor
The anti-symmetric part is known as vorticity
Basic Fluid Mechanics Concepts

Turbulent charge and turbulent current
–
The turbulent charge and turbulent current, collectively
referred to as turbulent sources, could substitute the
role of vorticity in more complicated flows.
Related Work

Multivalued data visualization
–
–
–
–

Flow visualization
–
–

“Feature-based” methods
Statistical methods
Icons
Layering
Spot noise
Line integral convolution
Computer graphics painting
Visualization Methodology

Developing a visualization method involves
–
–
–
Breaking the data into components
Exploring the relationships among components
Visually expressing both the components and
their relationships
Example 1: Rate of Strain Tensor

Data breakdown
Visualization design

–
–
Priority

Velocity

Vorticity
Layering

Primer

Underpainting

Ellipse layer

Arrow layer

Mask layer
Example 1: Rate of Strain Tensor
Simulated 2D flow past a cylinder at
Reynolds number = 100
Example 1: Rate of Strain Tensor
Simulated 2D flow past a cylinder at
Reynolds number = 500
Example 1: Rate of Strain Tensor
Experimental 2D flow past an airfoil
Example 2: Turbulent Charge and Turbulent current

Drag reduction (riblets)
Data breakdown
Visualization design


–
–
Priority

Overall location of the turbulent charge

Vorticity

Structure of the flow – velocity field

Fine details
Layering


Primer and underpainting
Arrow layer


Turbulent source layer
Mask layer
Example 2: Turbulent Charge and Turbulent current
Turbulent charge and turbulent current of
simulated 2D flow past a cylinder at Reynolds
number = 500
Example 2: Turbulent Charge and Turbulent current
Reynolds
number = 100
Example 2: Turbulent Charge and Turbulent current
Reynolds
number = 500
Example 2: Turbulent Charge and Turbulent current
Combination of
velocity, vorticity,
rate of strain,
turbulent charge
and turbulent
current for
Reynolds
number = 100
Summary and Conclusions

Borrow concepts from oil painting
–
–
–



Underpainting
Brush strokes
Layering
Represent many values at each spatial location in
different perspectives
Get a complete idea of both the dynamics and
kinematics of the flow
Provide catalyst for future understanding of more
complex fluid phenomena
Thank you!