(一)Particle-in-Cell Methods（PIC）Idea:–Particles handle advection trivially–Grids handle interactions efficientlyPut the two together:
-transfer quantities to grid
-solve on grid (interaction forces)
-transfer back to particles
-move particles (advection)Step:•Start with particles•Transfer to grid•Resolve forces on grid–Gravity, boundaries, pressure, etc.•Transfer velocity back to particles •Advect: move particles（二）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