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Particle-in-Cell Methods

Particle-in-Cell Methods. As per [Zhu&Bridson’05]. Particle-in-Cell Methods. Back to Harlow in the 1950’s for compressible flow Abbreviated “PIC” Idea: Particles handle advection trivially Grids handle interactions efficiently

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Particle-in-Cell Methods

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  1. Particle-in-Cell Methods As per [Zhu&Bridson’05]

  2. Particle-in-Cell Methods • Back to Harlow in the 1950’s 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)

  3. 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

  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

  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. 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 [Zhu&Bridson’05]: • Do it with a MAC grid pressure solve

  9. Where’s 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 can’t see/respond to small-scale particle variations – can potentially grow in time • Regularize: e.g. 95% FLIP, 5% PIC

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

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