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