Computational Fluid Dynamics Techniques: Modeling & Simulation for Animation

Computer AnimationAlgorithms and Techniques Computational Fluid Dynamics

Fluids conservation of mass momentum energy types viscous v. non-viscous compressible v. incompressible properties characteristics velocity laminar flow density turbulent pressure steady state flow heat gravity

d d d d d d d d d d d d d d d d Models grid-based (Eulerian) particle-based (Lagrangian) Hybrid

Notation Gradient Divergence

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

Conservation of Mass dx

Conservation of Mass If incompressible:

Conservation of Momentum in x dy dx

Conservation of Momentum

Velocity: u,v Coordinates: x,y Density: Pressure: p Euler Equations - 2D

Euler Equations - incompressible form

Stable Fluids Velocity grid Density grid Move densities around using velocity grid and dissipate densities Move velocities around using velocity grid and dissipate velocities

Stable Fluids Source Force Dissipation Advection

Computational Fluid Dynamics Techniques: Modeling & Simulation for Animation

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