Particle-in-Cell Methods

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Particle-in-Cell Methods

• As per ZhuBridson05

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Particle-in-Cell Methods

• Back to Harlow in the 1950s for compressible
  flow
• Abbreviated PIC
• Idea
• Particles handle advection trivially
• Grids handle interactions efficiently
• Put the two together-transfer quantities to
  grid-solve on grid (interaction
  forces)-transfer back to particles-move
  particles (advection)

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PIC

• Start with particles
• Transfer to grid
• Resolve forces on grid
• Gravity, boundaries, pressure, etc.
• Transfer velocity back to particles
• Advect move particles

• Start with particles
• Transfer to grid
• Resolve forces on grid
• Gravity, boundaries, pressure, etc.
• Transfer velocity back to particles
• Advect move particles

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PIC

• Start with particles
• Transfer to grid
• Resolve forces on grid
• Gravity, boundaries, pressure, etc.
• Transfer velocity back to particles
• Advect move particles

• Start with particles
• Transfer to grid
• Resolve forces on grid
• Gravity, boundaries, pressure, etc.
• Transfer velocity back to particles
• Advect move particles

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PIC

• Start with particles
• Transfer to grid
• Resolve forces on grid
• Gravity, boundaries, pressure, etc.
• Transfer velocity back to particles
• Advect move particles

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PIC

• Start with particles
• Transfer to grid
• Resolve forces on grid
• Gravity, boundaries, pressure, etc.
• Transfer velocity back to particles
• Advect move particles

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PIC

• Start with particles
• Transfer to grid
• Resolve forces on grid
• Gravity, boundaries, pressure, etc.
• Transfer velocity back to particles
• Advect move particles

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FLuid-Implicit-Particle (FLIP)

• Problem with PIC
• We resample (average) twice
• Even more numerical dissipation than pure
  Eulerian methods!
• FLuid-Implicit-Particle (FLIP) Brackbill
  Ruppel 86
• Transfer back the change of a quantity from grid
  to particles, not the quantity itself
• Each delta only averaged once no accumulating
  dissipation!
• Nearly eliminated numerical dissipation from
  compressible flow simulation
• Incompressible FLIP ZhuBridson05
• Do it with a MAC grid pressure solve

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Wheres the Catch?

• Accuracy
• When we average from particles to grid, simple
  weighted averages is only first order
• Not good enough for level sets
• Noise
• Typically use 8 particles per grid cell for
  decent sampling
• Thus more degrees of freedom in particles then
  grid
• The grid simulation cant see/respond to
  small-scale particle variations can potentially
  grow in time
• Regularize e.g. 95 FLIP, 5 PIC

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Movies

• PIC vs. FLIP in 2d (marker particles)
• 3d examples (marker particles implicit surface)