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Visual Simulation of Smoke
SIGGRAPH’01
Ronald Fedkiw, Jos Stam and Henrik Wann Jensen
Stanford University & Alias|wavefront
Outline
Introduction Previous Work The Equations of Fluid Flow Self-Advection by Semi-Lagrangian Numerical Dissipation Results
Introduction
Ideally Looks good Fast simulation
Looks good? Needs to look plausible Doesn’t need to be exactly correct doesn’t suffer from excessive numerical
dissipation
Previous Work
Kajiya and Von Herzen (SIGGRAPH 84) N. Foster and D. Metaxas (SIGGRAPH 97) Improve Stam’99 (Stable Fluids)
Handle moving boundaries Reduce numerical dissipation Add high quality volume rendering
Method still fast but looks more “smoke-like”
The Equations of Fluid FlowReview:Navier-Stokes Equations
Incompressible Euler Equations
self-advection forces
0 uincompressible
(Navier-Stokes without viscosity)
Fluid velocity:u= <Vu , Vv , Vw >
Gradient Implement
Additional Equations
)(
ut
Tut
T)(
zTTzf amb )(
Density
Temperature
Buoyancy force
Algorithm
t=0 t = t + dt
add forces self-advection project
0 u
Helmholtz-Hodge Decomposition
Self-Advection
t t+dt
Semi-Lagrangian solver (Courant, Issacson & Rees 1952)
)( u
Semi- Lagrangian
The semi-Lagrangian integrator itself is broken down into three main parts
1. Vector field extraction
2. Particle tracing
3. Interpolation
Self-Advection
t t+dt
Semi-Lagrangian solver (Courant, Isaacson & Rees 1952)
Self-Advection
t t+dt
For each u-component…
Self-Advection
t t+dt
For each u-component…
Self-Advection
t t+dt
Set interpolated value in new grid
Self-Advection
Repeat for all u-nodes
Self-Advection
Repeat for all v-nodes
Numerical Dissipation
‘Stable Fluids’ method dampens the flow Typical with semi- Lagrangian
methods
Improve using “Vorticity Confinement” force
Vorticity Confinement
Basic idea: Add energy lost as an external force
Use “Vorticity Confinement” force invented by John Steinhoff 1994
Vorticity Confinement
2
1)(
2
1
y
u
x
uu xy
: vorticity
Vorticity Confinement
Vorticity location vector : Normalized vorticityLocation vector : N
Vorticity Confinement
Spatial discretization:h
Total Forces
User supplied fields
Buoyancy force
New confinement force
Results
Results
Any Problem?
