1. Visual Simulation of Smoke
Based on Jos Stam’s SIGGRAPH’01 presentation
Represented by
Justin Hensley

2. Smoke in computer graphics
Ideally
Looks good
Fast simulation
Looks good?
Needs to look plausible
Doesn’t need to be exactly correct

3. Stam’01 model Improve Stam’99 (Stable Fluids)
Handle moving boundaries
Reduce numerical dissipation
Add high quality volume rendering
Method still fast but looks more “smoke-like”

4. Incompressible Euler Equations
self-advection
forces
Fluid velocity:
u= <Vu , Vv , Vw >
incompressible
(Navier-Stokes without viscosity)

5. Additional Equations
density
temperature
buoyancy
force

6. Algorithm
add forces self-advect project
t=0
t = t + dt

7. Self-Advection t
t+dt
Semi-Lagrangian solver (Courant, Issacson & Rees 1952)

8. Semi-What? What’s the semi in Semi-Lagrangian? Lagrangian method
Both mesh and flow moves
Semi-Lagrangian method
Mesh is held constant
Flow is advected
Allows for easy interpolation of values when bact tracing.

9. Self-Advection t
t+dt
Semi-Lagrangian solver (Courant, Issacson & Rees 1952)

10. Self-Advection t
t+dt
For each u-component…

11. Self-Advection t
t+dt
For each u-component…

12. Self-Advection t
t+dt
Set interpolated value in new grid

13. Self-Advection
Repeat for all u-nodes

14. Self-Advection
Repeat for all v-nodes

15. Self-Advection
Vmax > Vmax
Advected velocity field

16. Moving objects

17. Moving objects

18. Moving objects

19. Moving objects

20. Moving objects

21. Moving objects

22. Moving objects

23. Numerical Dissipation
‘Stable Fluids’ method dampens the flow
Typical with semi- Lagrangian methods
Improve using
“Vorticity Confinement” force
monotonic cubic interpolation

24. Vorticity Confinement
Basic idea:
Add energy lost as an external force
Use “Vorticity Confinement” force
invented by John Steinhoff ~10 years ago

25. Vorticity Confinement

26. Vorticity Confinement
Vorticity location
vector : 
Normalized vorticity
Location vector : N

27. Vorticity Confinement
Amount of detail
added back :  (> 0)
Spatial discretization: h

28. Results

29. Results