ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow...
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Transcript of ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow...
![Page 1: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/1.jpg)
ENV 2006 15.1
Envisioning Information
Lecture 15 – Scientific Visualization
Vector Data – Flow Visualization
![Page 2: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/2.jpg)
ENV 2006 15.2
• The major application area is Computational Fluid Dynamics where we wish to visualize the velocity field within a volume, or on a surface
• ... but has applications to any other discipline where flowflow is involved– for example, the flow of population in social sciences
• Important distinction between steady and unsteady (time-dependent) flow
Applications of Vector Field Visualization
![Page 3: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/3.jpg)
ENV 2006 15.3
Virtual Windtunnel
The VirtualWindtunnel isa VR facilitydevelopedby NASA foraircraft testing
![Page 4: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/4.jpg)
ENV 2006 15.4
Visualizing Flow over Aircraft Wing
![Page 5: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/5.jpg)
ENV 2006 15.5
• Experimental fluid dynamics:– aim to get impression of flow around a scale model of object
(eg smoke in wind tunnel)
– disadvantages in cost, time and integrity
• Computational fluid dynamics– simulation of the flow (Navier-Stokes equations)
– visualization of the resulting velocity field so as to mimic the experimental techniques
Experimental and Computational Fluid Dynamics
![Page 6: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/6.jpg)
ENV 2006 15.6
• Time lines– row of small particles (hydrogen bubbles) released at right
angles to flow
– motion of ‘line’ shows the fluid flow
• Streak line– dye injected from fixed position for period of time
– tracer of dye shows the fluid flow
• Path line– small particles (magnesium powder in liquid; oil drops in gas)
– velocity measured by photographing motion with known exposure time
Experimental Flow Visualization – Adding Foreign Material
![Page 7: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/7.jpg)
ENV 2006 15.7
• Visualization of flow field on surface of object achieved by fixing tufts at several points on surface - orientation of threads indicates direction of flow
• Notice distinction: – tufts show flow past a fixed point (Eulerian)
– bubbles etc show the flow from point of view of a floating object (Lagrangian)
Experimental Flow Visualization – Other Techniques
![Page 8: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/8.jpg)
ENV 2006 15.8
Experimental Visualization Example - Poster Paint in Water
see www.flometrics.com
![Page 9: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/9.jpg)
ENV 2006 15.9
Experimental Visualization - Particles Illuminated by Laser Sheet Light
![Page 10: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/10.jpg)
ENV 2006 15.10
• Now look at methods for computer aided flow visualization• Assume initially velocity field given on 3D Cartesian grid
velocityvx, vy, vz
given at each grid point
hexahedralcells
Computational Flow Visualization
![Page 11: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/11.jpg)
ENV 2006 15.11
• Sometimes it is useful to derive scalar quantities from the velocity field
• For example, velocity magnitude– speed = sqrt (vx
2 + vy2 + vz
2)
• How would these be visualized?
Using Scalar Techniques
![Page 12: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/12.jpg)
ENV 2006 15.12
• Very simple technique• Arrow drawn at each grid point showing direction and size of
velocity
This works effectivelyenough in 2D
Arrows
![Page 13: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/13.jpg)
ENV 2006 15.13
• But in 3D it suffers from perception problems:
Is it this?
or this?
Of course the picture quickly gets cluttered too
Arrows
![Page 14: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/14.jpg)
ENV 2006 15.14
• Arrows can be used successfully in 3D as follows:– by slicing the volume, and attaching arrows (with shadow effects) to
the slice plane - this gives a hedgehog effect
– by giving more spatial cues - drawing arrows as true 3D objects
but clutter again a problem!
{BTW - Eulerian or Lagrangian?}
Arrows
![Page 15: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/15.jpg)
ENV 2006 15.15
CFD simulation of laser example
Flometrics - see www.flometrics.com
![Page 16: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/16.jpg)
ENV 2006 15.16
Comparison of Experimental and Computational Visualization
![Page 17: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/17.jpg)
ENV 2006 15.17
Tufts
![Page 18: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/18.jpg)
ENV 2006 15.18
IRIS Explorer
• VectorDisplay module
![Page 19: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/19.jpg)
ENV 2006 15.19
• This is analogous to experimental path lines - we imagine following the path of a weightless particle - cf a bubble
• Suppose initial position - seed point - is(x0, y0, z0)
• The aim is to find how the path
( x(t), y(t), z(t) )
develops over time
• Also called particle advection
Particle Traces
![Page 20: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/20.jpg)
ENV 2006 15.20
Particle Traces
• Motion of a particle is given by:
dx/dt = vx; dy/dt = vy; dz/dt = vz
• Three ordinary differential equations with initial conditions at time zero:
x(0) = x0; y(0) = y0; z(0) = z0
In 2D, we have:
(x0,y0)
(vx,vy) israte of changeof position
![Page 21: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/21.jpg)
ENV 2006 15.21
Particle Tracing – Numerical Techniques for Solving the Flow Equations
• Simplest technique is Euler’s method:
dx/dt = ( x(t+t) - x(t)) / t = vx(p(t))
hence
x(t+t) = x(t) + t.vx(p(t))
• Similarly, for y(t) and z(t)
p = (x, y, z)
In 2D, we have:
(x0,y0)
(x1,y1)
(t.vx,t.vy)
![Page 22: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/22.jpg)
ENV 2006 15.22
Particle Tracing - Interpolation
• As the solution proceeds, we need velocity values at interior points
• (vx, vy, vz) is calculated at current point (x,y,z) - by trilinear interpolation for example.
In 2D, we have:
(x0,y0)
(x1,y1)(vx,vy) foundby interpolation(bilinear)
![Page 23: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/23.jpg)
ENV 2006 15.23
Particle Tracing - Point Location
• When we leave one cell, we need to determine which cell the new point belongs to
(x0,y0)
(x1,y1) -this is quitestraightforwardfor Cartesiangrids
![Page 24: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/24.jpg)
ENV 2006 15.24
Particle Tracing - Algorithm
find cell containing initial position
{point location}
while particle in grid
determine velocity at current position
{interpolation}
calculate new position
{integration}
find cell containing new position
{point location}
endwhile
![Page 25: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/25.jpg)
ENV 2006 15.25
Improving the Integration
• Euler’s method is inaccurate (unless the step size t is very small)
• Better is Runge-Kutta:– x* = x(t) + t.vx(p(t)) (and for y*, z*)– x(t+t) = x(t) + t.{ vx(p(t)) + vx(p*)}/2 (and for y,z)
• This is Runge-Kutta 2nd order - there is also a more accurate 4th order method
• There is another source of error in particle tracing– what?
![Page 26: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/26.jpg)
ENV 2006 15.26
• Particles may be rendered as– points - but are there better representations?
• It is common to use a rake of seed points, rather than just one - rake can be line, circle, even an area...
Rendering the Particles – and Rakes
![Page 27: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/27.jpg)
ENV 2006 15.27
Particle Advection Example - Flow Around a Moving Car
Created usingIRIS Explorer
![Page 28: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/28.jpg)
ENV 2006 15.28
Flow Visualization by Particle Tracing in IRIS Explorer
• Look at the following modules:
– NAGAdvectSimple– NAGAdvectAnimate
![Page 29: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/29.jpg)
ENV 2006 15.29
• Streak lines– release continuous flow of particles for a short period
• Time lines– release a line of particles at same instant and draw a curve through
the positions at successive time intervals
Streak Lines and Time Lines
![Page 30: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/30.jpg)
ENV 2006 15.30
• Mathematically, stream lines are lines everywhere tangential to the flow
• For a steady flow - what is the relation between stream lines and particle traces?
stream lines
Stream Lines
![Page 31: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/31.jpg)
ENV 2006 15.31
• In 3D, curves are hard to understand without depth cues• Ideas used include:
– stream ribbons - each streamline drawn as a thin flat ribbon, showing twist; or two adjacent streamlines connected into ribbon, showing twist and divergence
– tubes
Rendering Streamlines
![Page 32: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/32.jpg)
ENV 2006 15.32
Streamlines Example
Streamlines drawn as tubes - by K Ma of ICASE (see www.icase.edu)
![Page 33: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/33.jpg)
ENV 2006 15.33
• Streamlines and stream ribbons best for flow direction• Particle traces best for flow speed• Note that derived quantities are also visualized:
– flow speed as 3D scalar field– vorticity field as 3D vector field– vorticity magnitude as 3D scalar field(Vortex = rotational flow about axisvorticity = vector product of velocity and its gradient)
Steady Flow Visualization
![Page 34: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/34.jpg)
ENV 2006 15.34
• Recent research interest has been in the more complex case of unsteady flows, where velocity depends on time
• Particle traces, streak lines and time lines can all be used• Streak lines seem to give the best results• Nice applet at:
http://widget.ecn.purdue.edu/~meapplet/java/flowvis/Index.html
Unsteady Flow Visualization
![Page 35: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/35.jpg)
ENV 2006 15.35
• A new class of image-based methods attempts to visualize flow as a texturing effect
• Most successful for 2D flow - and also for flow over surfaces in 3D
• Methods include:– line integral convolution - lic
Flow Visualization – Texture Effects
![Page 36: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/36.jpg)
ENV 2006 15.36
• Essence of method is:– consider a white noise texture, T(x,y)
– for each pixel, set its intensity as a function (eg average) of values of T along a short streamline segment through the pixel
– this has effect of correlating the resulting pixel values along streamlines, so a sense of the flow direction is obtained
whitenoise
flowlines
LIC
Line Integral Convolution (LIC)
![Page 37: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/37.jpg)
ENV 2006 15.37
LIC Example
Flow over surface of car - from CIRA, ItalyItalian Aerospace Research Centre
![Page 38: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/38.jpg)
ENV 2006 15.38
LIC Example
Flow underneath car - from CIRA, Italy
![Page 39: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/39.jpg)
ENV 2006 15.39
LIC Example – Wind Flow over Surface of Norwegian Fjord
From Zoran Constantinescuhttp://www.idi.ntnu.no/~zoran/
![Page 40: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/40.jpg)
ENV 2006 15.40
LIC Movie
![Page 41: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/41.jpg)
ENV 2006 15.41
IRIS Explorer LIC
• Look at the module LatLIC
![Page 42: ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk.](https://reader035.fdocuments.us/reader035/viewer/2022062511/5515f4a5550346d46f8b5591/html5/thumbnails/42.jpg)
ENV 2006 15.42
Image-based Methods over Surfaces