Particle-in-Cell Methods - PowerPoint PPT Presentation

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Particle-in-Cell Methods

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transfer back to particles -move particles (advection) Start with ... Transfer velocity back to particles. Advect: move particles. Start with particles ... – PowerPoint PPT presentation

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Title: Particle-in-Cell Methods


1
(No Transcript)
2
Particle-in-Cell Methods
  • As per ZhuBridson05

3
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)

4
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

5
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

6
PIC
  • Start with particles
  • Transfer to grid
  • Resolve forces on grid
  • Gravity, boundaries, pressure, etc.
  • Transfer velocity back to particles
  • Advect move particles

7
PIC
  • Start with particles
  • Transfer to grid
  • Resolve forces on grid
  • Gravity, boundaries, pressure, etc.
  • Transfer velocity back to particles
  • Advect move particles

8
PIC
  • Start with particles
  • Transfer to grid
  • Resolve forces on grid
  • Gravity, boundaries, pressure, etc.
  • Transfer velocity back to particles
  • Advect move particles

9
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

10
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

11
Movies
  • PIC vs. FLIP in 2d (marker particles)
  • 3d examples (marker particles implicit surface)
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