1. Procedural Animation Lecture 11: Fluid dynamics
Procedural Methods in 3D Computer Animation
Dr. Midori Kitagawa

2. Procedural Animations
Two major categories in procedural animation are:
Physics-based simulations deal with things that are not alive
Alife (artificial life) deals with things are virtually alive

3. Physics-based simulations
Deal with the things that are not alive. Use well-known natural physical laws.
Particle systems
Rigid body dynamics
Soft body dynamics
Pyro with volume model
Fluid dynamics
Fur/hair

4. Fluid dynamics
Generate realistic animations of fluids for FX, animation and games.
Different from computational fluid dynamics to study the behavior of fluids.

5. Fluid dynamics Eulerian representation – grid-based
Lagrangian representation – particle based \

6. Eulerian vs Lagrangian
Leonhard Euler ( ) born in Switzerland; died in Russia
Joseph-Louis Lagrange ( ) born in Sardina (Italy); died in France
grid based vs. particle based

7. Lagrangian vs Eulerian
Eulerian keeps track of changes in a spatially fixed volume.
Lagrangian follows particles in their motion.

8. Eulerian representation
Fluid is represented in a domain that is divided into small cells.
Accurate calculation in low density areas.
Fluid cannot spread out freely in space.
A large number of cells are need to capture surface details.

9. Lagrangian representation
Fluid is represented as a collection of particles.
Fluid flow is simulated by particle dynamics.
Intuitive.
Fluid can spread freely in space.
Inaccurate calculation in low density areas.
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques Pages 15-22 

10. FLIP (Fluid Implicit Particle) method
Hybrid method which uses both grids and particles.
Initialize particle positions and velocities.
Transfer particles to a grid.
Apply external forces.
Classify all voxels as fluid, solid or air.
Update particle velocities.
Update particle positions.
Go back to Step 2.
Reconstruct a fluid surface for rendering.
“Animating Sand as a Fluid”

11. Houdini FLIP
Cache!