681 Introduction to Computer Graphics (PowerPoint download)

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					            Computer Animation
         Algorithms and Techniques
              Computational Fluid Dynamics




Rick Parent                                  Computer Animation
  Fluids

                                     conservation of
    types
    viscous v. non-viscous           mass
    compressible v. incompressible   momentum
                                     energy


       characteristics                 properties
       laminar flow                    velocity
                                       density
       turbulent
                                       pressure
       steady state flow
                                       heat
                                       gravity

Rick Parent                                 Computer Animation
  Models                        d   d   d   d
                                d   d   d   d
                                d   d   d   d
   grid-based (Eulerian)        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
                           Velocity: u,v
    Euler Equations - 2D   Coordinates: x,y
                           Density:
                           Pressure: p




Rick Parent                  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   Advection




Rick Parent                               Computer Animation

				
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