The document discusses fluid simulation and control in computer graphics, focusing on the differences between computational fluid dynamics and graphic fluid simulation needs. It emphasizes the importance of achieving visually plausible results within production constraints while providing insight into the mathematical and algorithmic approaches used for guided fluid simulation. The work highlights challenges and solutions in computational modeling to successfully navigate between high-resolution and low-resolution fluid simulations.

1. Fluid Simulation and Control for
Computer Graphics
Michael Bang Nielsen
Aarhus University

2. What is Computer Graphics?
• Modeling
– Geometry
– Appearance
• Animation
– Keyframes
– Motion Capture
– Simulation/Synthesis
• Rendering
– Offline
– Realtime

3. What is Physically Based
Animation?
• Rigid bodies
• Deformable objects
• Cloth
• Hair
• Fluids
– Water
– Smoke
– Fire
– Air
Important for games, but what about movies and commercials?

4. Why Computer Generated Effects
for Movies and Commercials?
Real world smoke and water phenomena are very complex

5. Why Computer Generated Effects
for Movies and Commercials?
Ivan Aivazovsky, ”The Ninth Wave”, 1850.
It requires remarkable talent and a lot of time to do..

6. Why Computer Generated Effects
for Movies and Commercials?
From Rikitt: Special Effects
And real phenomena have scale…

7. Why Computer Generated Effects
for Movies and Commercials?
From Rikitt: Special Effects
And real phenomena have scale…

8. Why Computer Generated Effects
for Movies and Commercials?
Copyright Cinefex.
But sometimes physical effects work.

9. State of the Art in Fluid Simulation
for Computer Graphics
1: http://www.scanlinevfxla.com/la/en/reels.html
2: Sequence from Golden Compass
Molemaker et al.

10. State of the Art in Fluid Simulation
for Computer Graphics
Sequence from Day After Tomorrow:
Copyright Twentieth Century Fox.
But don’t be fooled: Artists spend
a lot of time making raw simulations look good

11. How do we Simulate Fluids for
Computer Graphics?
From John D. Anderson: Computational Fluid Dynamics
Math, Physics, Computer Science, Fluid Dynamics
and Computational Fluid Dynamics (CFD)

12. Fluid Simulation for Computer
Graphics
Demands are different than in CFD:
• Should be
visually plausible
• Physical accuracy
not paramount
• Animators/director
want a certain
visual style

13. Fluid Simulation for Computer
Graphics
• Simulation speed –
deadlines and
interactive preview
• The fluid should have
character
Production designs by Jon Brooks
• The artists want
control – it should be
possible to sculpt the
fluid
From Inkheart. Image by Double Negative

14. Guided Fluid Simulation
Collaboration between
• Michael Bang Nielsen
• Brian Bunch Christensen
• Nafees Bin Zafar
• Doug Roble
• Ken Museth
I will share both our successes and frustrations with you!

15. Guided Fluid Simulation
Motivation
Our Contribution:
Coarse Simulation Guided Fine Simulation
Fine Simulation

16. Guided Fluid Simulation
Motivation
High Res Low Res Low Res Upsampled

17. Guided Fluid Simulation
Problem Statement
Develop
• Mathematical model
• Algorithms
• Data structures
That make it possible to guide a
high resolution fluid simulation
using a low resolution simulation

18. Guided Fluid Simulation
The Fundamental Idea
The low frequencies of the fine
simulation should be equal to the
frequencies of the coarse simulation
Challenge: Formulate this mathematically

19. The One-Slide Fluid Mechanics
Course
Net force = mass x acceleration
F = ma ⇒ F
Vol
=a
m
Vol
⇒ 1 F
ρ Vol
=a

20. The One-Slide Computational Fluid
Mechanics Course
In computer graphics we apply Operator Splitting:
Advection
Body forces
Incompressibility

21. Guided Fluid Simulation
How do we attack the problem?
Advection
Body forces
Incompressibility
The low frequencies of the fine
simulation should be equal to the
frequencies of the coarse simulation

22. Guided Fluid Simulation
The Force-Based Approach
• Forces (all or low frequencies)
Thuerey et al.
• Blending of divergence free velocity fields
– Leads to results that are too smooth

23. Guided Fluid Simulation
How do we attack the problem?
Advection
Body forces
Incompressibility
The low frequencies of the fine
simulation should be equal to the
frequencies of the coarse simulation

24. Guided Fluid Simulation
The Modified Pressure Projection
Approach
Observation
Solving for Incompressibility
is identical to the minimization of
subject to the constraint

25. Guided Fluid Simulation
The Modified Pressure Projection
Approach
We add the constraint
to the minimization of
subject to the constraint

26. Guided Fluid Simulation
The Modified Pressure Projection
Approach
Calculus of variations leads to the equations
Does it work?

27. Guided Fluid Simulation
The Modified Pressure Projection
Approach
Test-simulations in Matlab
Problems:
• Matrix singular when filter is wide
• Where should we place the constraints?

28. Guided Fluid Simulation
The Modified Pressure Projection
Approach
Fundamental question:
Does our approach fail completely,
or can we modify it somehow?

29. Guided Fluid Simulation
The Modified Pressure Projection
Second Approach
The low frequencies of the fine
simulation should be as close as
possible to the frequencies of the
coarse simulation
Challenge: Formulate this mathematically

30. Guided Fluid Simulation
The Modified Pressure Projection
Second Approach
We add the minimization term
to the minimization of
subject to the constraint

31. Guided Fluid Simulation
The Modified Pressure Projection
Second Approach
Calculus of variations leads to the equations
Does it work?

32. Guided Fluid Simulation
The Modified Pressure Projection
Second Approach
Verification in 2D

33. Guided Fluid Simulation
The Modified Pressure Projection
Second Approach
Fast to solve, but 1602 requires roughly 2GB and we want to
do it in 2563…

34. Guided Fluid Simulation
The Modified Pressure Projection
Second Approach
Computational challenges:
• Sparse entries take up 4.04TB in resolution 2563
• We reduced this to 208MB
• Linear system is a-symmetric
• Solution: Improved multigrid solver
• Linear system is slow to solve
• Solution: Parallel solver using separable lowpass filters

35. Guided Fluid Simulation
The Modified Pressure Projection
Second Approach
More computational challenges:
• Boundaries traditionally hard to use with
multigrid
• Which lowpass filter should be used?
• How do we handle non-physically based
guiding velocity fields?

36. Results
Interpolation between strictly guided and unguided simulation
Low res High Res

37. Links to More Information
• http://cs.au.dk/research/areas/computer-
graphics-and-scientific-computing/
• http://cg.alexandra.dk/2009/05/15/smoke-
rendering-demo/