Transcript Simulating Smokes

Visual Simulation
of Smoke
Based on Jos Stam’s
SIGGRAPH’01 presentation
Represented by
Justin Hensley
Smoke in computer
graphics

Ideally
Looks good
 Fast simulation


Looks good?
Needs to look plausible
 Doesn’t need to be exactly correct

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”
Incompressible Euler
Equations
self-advection
Fluid velocity:
u= <Vu , Vv , Vw >
forces
u  0
incompressible
(Navier-Stokes without viscosity)
Additional Equations
density
temperature
buoyancy
force

 (u  ) 
t
T
 (u  )T
t
f  z   (T  Tamb ) z
Algorithm
add forces
t=0
self-advect
project
t = t + dt
Self-Advection
t
t+dt
Semi-Lagrangian solver (Courant, Issacson & Rees 1952)
Semi-What?

What’s the semi in SemiLagrangian?

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.
Self-Advection
t
t+dt
Semi-Lagrangian solver (Courant, Issacson & Rees 1952)
Self-Advection
t
For each u-component…
t+dt
Self-Advection
t
For each u-component…
t+dt
Self-Advection
t
Set interpolated value in new grid
t+dt
Self-Advection
Repeat for all u-nodes
Self-Advection
Repeat for all v-nodes
Self-Advection
Vmax
>
Vmax
Advected velocity field
Moving objects
Moving objects
Moving objects
Moving objects
Moving objects
Moving objects
Moving objects
Numerical Dissipation

‘Stable Fluids’ method dampens
the flow
 Typical with semi- Lagrangian
methods

Improve using
“Vorticity Confinement” force
 monotonic cubic interpolation

Vorticity Confinement

Basic idea:


Add energy lost as an external
force
Use “Vorticity Confinement” force

invented by John Steinhoff ~10
years ago
Vorticity Confinement
 : vorticity
  u
Vorticity Confinement
Vorticity location
vector : 
Normalized vorticity
Location vector : N
Vorticity Confinement
Amount of detail
added back :  (> 0)
Spatial discretization:
h
Results
Results