1. ENV 200615.1 Envisioning Information Lecture 15 – Scientific Visualization Vector Data – Flow Visualization Ken Brodlie kwb@comp.leeds.ac.uk

2. ENV 200615.2 The major application area is Computational Fluid Dynamics where we wish to visualize the velocity field within a volume, or on a surface flow... but has applications to any other discipline where flow 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

3. ENV 200615.3 Virtual Windtunnel The Virtual Windtunnel is a VR facility developed by NASA for aircraft testing

4. ENV 200615.4 Visualizing Flow over Aircraft Wing

5. ENV 200615.5 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

6. ENV 200615.6 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

7. ENV 200615.7 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

8. ENV 200615.8 Experimental Visualization Example - Poster Paint in Water see www.flometrics.com

9. ENV 200615.9 Experimental Visualization - Particles Illuminated by Laser Sheet Light

10. ENV 200615.10 Now look at methods for computer aided flow visualization Assume initially velocity field given on 3D Cartesian grid velocity v x, v y, v z given at each grid point hexahedral cells Computational Flow Visualization

11. ENV 200615.11 Sometimes it is useful to derive scalar quantities from the velocity field For example, velocity magnitude –speed = sqrt (v x 2 + v y 2 + v z 2 ) How would these be visualized? Using Scalar Techniques

12. ENV 200615.12 Very simple technique Arrow drawn at each grid point showing direction and size of velocity This works effectively enough in 2D Arrows

13. ENV 200615.13 But in 3D it suffers from perception problems: Is it this? or this? Of course the picture quickly gets cluttered too Arrows

14. ENV 200615.14 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

15. ENV 200615.15 CFD simulation of laser example Flometrics - see www.flometrics.com

16. ENV 200615.16 Comparison of Experimental and Computational Visualization

17. ENV 200615.17 Tufts

18. ENV 200615.18 IRIS Explorer VectorDisplay module

19. ENV 200615.19 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 (x 0, y 0, z 0 ) The aim is to find how the path ( x(t), y(t), z(t) ) develops over time Also called particle advection Particle Traces

20. ENV 200615.20 Particle Traces Motion of a particle is given by: dx/dt = v x ; dy/dt = v y ; dz/dt = v z Three ordinary differential equations with initial conditions at time zero: x(0) = x 0 ; y(0) = y 0 ; z(0) = z 0 In 2D, we have: (x 0,y 0 ) (v x,v y ) is rate of change of position

21. ENV 200615.21 Particle Tracing – Numerical Techniques for Solving the Flow Equations Simplest technique is Eulers method: dx/dt = ( x(t+ t) - x(t)) / t = v x (p(t)) hence x(t+ t) = x(t) + t.v x (p(t)) Similarly, for y(t) and z(t) p = (x, y, z) In 2D, we have: (x 0,y 0 ) (x 1,y 1 ) ( t.v x, t.v y )

22. ENV 200615.22 Particle Tracing - Interpolation As the solution proceeds, we need velocity values at interior points (v x, v y, v z ) is calculated at current point (x,y,z) - by trilinear interpolation for example. In 2D, we have: (x 0,y 0 ) (x 1,y 1 ) (v x,v y ) found by interpolation (bilinear)

23. ENV 200615.23 Particle Tracing - Point Location When we leave one cell, we need to determine which cell the new point belongs to (x 0,y 0 ) (x 1,y 1 ) -this is quite straightforward for Cartesian grids

24. ENV 200615.24 Particle Tracing - Algorithm find cell containing initial position {point location} whileparticle in grid determine velocity at current position {interpolation} calculate new position {integration} find cell containing new position {point location} endwhile

25. ENV 200615.25 Improving the Integration Eulers method is inaccurate (unless the step size t is very small) Better is Runge-Kutta: –x* = x(t) + t.v x (p(t)) (and for y*, z*) –x(t+ t) = x(t) + t.{ v x (p(t)) + v x (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?

26. ENV 200615.26 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

27. ENV 200615.27 Particle Advection Example - Flow Around a Moving Car Created using IRIS Explorer

28. ENV 200615.28 Flow Visualization by Particle Tracing in IRIS Explorer Look at the following modules: –NAGAdvectSimple –NAGAdvectAnimate

29. ENV 200615.29 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

30. ENV 200615.30 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

31. ENV 200615.31 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

32. ENV 200615.32 Streamlines Example Streamlines drawn as tubes - by K Ma of ICASE (see www.icase.edu)

33. ENV 200615.33 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 axis vorticity = vector product of velocity and its gradient) Steady Flow Visualization

34. ENV 200615.34 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

35. ENV 200615.35 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

36. ENV 200615.36 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 white noise flow lines LIC Line Integral Convolution (LIC)

37. ENV 200615.37 LIC Example Flow over surface of car - from CIRA, Italy Italian Aerospace Research Centre

38. ENV 200615.38 LIC Example Flow underneath car - from CIRA, Italy

39. ENV 200615.39 LIC Example – Wind Flow over Surface of Norwegian Fjord From Zoran Constantinescu http://www.idi.ntnu.no/~zoran/

40. ENV 200615.40 LIC Movie

41. ENV 200615.41 IRIS Explorer LIC Look at the module LatLIC

42. ENV 200615.42 Image-based Methods over Surfaces