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AC274: Particles in Cell ( phase-space fluids)

AC274: Particles in Cell ( phase-space fluids). Phase-space fluids. S ystems with soft (long- range ) interations : Grazing collisions (small deflections ) Each particle feels a collective soft interaction. Plasmas , A strophysics Biological fluids , Electrophoresis ,.

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AC274: Particles in Cell ( phase-space fluids)

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  1. AC274: Particles in Cell (phase-space fluids)

  2. Phase-spacefluids Systems with soft (long-range) interations: Grazing collisions (small deflections) Eachparticlefeels a collective soft interaction Plasmas, Astrophysics Biologicalfluids, Electrophoresis,

  3. Particle-Particle: hard-core Field-Particle: smooth Particle: mesh-free Field: mesh bound

  4. Electro-biofluids: IonChannels

  5. Vlasov-Poisson-Boltzmann

  6. Superparticles

  7. Lengthscales and resolution Smooth force:

  8. PIC: solution procedure • Charge assign to the grid (P2G) • Solve field eq.s on the grid (GG) • Compute forces on the particles (G2P) • Move particles (PP)

  9. G-P duality Charge Potential Force Transfer operators: Weight and Green P2G: G2P:

  10. PIC algorithm GG: Chargeassign: 2.GG: Solve Poisson:

  11. Vlasov-Poisson 3. GP: Force interpolation 4. PP: MoveParticles

  12. Chargeassign: scatter, P2G

  13. Solve Poisson, GG

  14. Potential to Force (GG)

  15. Force transfer G2P

  16. ParticleMover

  17. ChargeAssign: Locate Grid NW NE P=(x,y) SE SW

  18. Locatingparticles in arbitrarygrids

  19. ChargeAssign: NGP 3 2 P 0 1

  20. ChargeAssign: PWC NW NE P SW SE

  21. ChargeAssign: PWlin NE=2 NW=3 p=(x,y) b a SW=0 SE=1

  22. Force interp: NGP NW NE SW SE

  23. Force interp: PWC NW NE SW SE

  24. Force interp: PWL 2 3 p b 0 1 a

  25. Chargecollect: receive

  26. Chargeassign: NGP 7 6 8 5 3 1 4 2

  27. Chargeassign: PWC 7 6 8 5 3 1 4 2

  28. Shapefunctions: 1d

  29. SpuriousForces and GridIndependence

  30. The self-force problem

  31. The self-force problem ng=2

  32. The self-force problem

  33. Spuriousforces PwL: -a*(1-a)+(1-a)*a; = 0 for any a PwC: -a*1/2+(1-a)*1/2=1/2-a; = 0 only for a=1/2 NGP: -a*1, or (1-a)*1; = 0 never BUT: if <a>=1/2 bothpwc and ngpgive zero on average!

  34. Choosing the kernel Use the samekernel Or: Force kernel G equal or lowerorderthanchargekernelW

  35. Poisson solver

  36. Poisson Solver Spectral(ifyoucan…)

  37. Poisson Solver: relax

  38. Poisson Solver: RES Special case: Laplace

  39. Poisson Solver: bc TBD

  40. Thomas algorithm Bwdsweep Fwd sweep

  41. Thomas 2D  ADI    

  42. Particlemover

  43. Position Verlet Staggered: (4th, reversible) Q: How do we start-off?

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