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Download Simulating Smokes
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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
