Computer Animation Algorithms and Techniques

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Computer AnimationAlgorithms and Techniques
Computational Fluid Dynamics
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Fluid
viscous v. non-viscous
conservation of mass momentum energy
compressible v. non-compressible
laminar flow
turbulent
velocity
steady state flow
density
gravity
pressure
heat
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Models
grid-based (Eulerian)
particle-based (Lagrangian)
Hybrid
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Notation
Gradient
Divergence
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Divergence Theorem
The integral of the flow fields divergence over
the volume of the cell is the same as the intgral
of the flow field over the cells boundary
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Conservation of Mass
dx
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Conservation of Mass
If incompressible
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Conservation of Momentum
in x
dy
dx
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Conservation of Momentum
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Velocity u,v Coordinates x,y Density Pressure
p
Euler Equations - 2D
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Euler Equations - incompressible form
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Stable Fluids
Velocity grid
Density grid
Move densities around using velocity grid and
dissipate densities
Move velocities around using velocity grid and
dissipate velocities
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Stable Fluids
Source
Force
Advection
Dissipation