visual simulation of smoke siggraph’01 ronald fedkiw, jos stam and henrik wann jensen stanford...
Post on 21-Dec-2015
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TRANSCRIPT
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”
Incompressible Euler Equations
self-advection forces
0 uincompressible
(Navier-Stokes without viscosity)
Fluid velocity:u= <Vu , Vv , Vw >
Semi- Lagrangian
The semi-Lagrangian integrator itself is broken down into three main parts
1. Vector field extraction
2. Particle tracing
3. Interpolation
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