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PIC/FLIP (Material Point Method)
Mix between particles and grid based approach.
- Particles: good for advection
- Grid: forces, pressure, viscosity
\(u_p\): velocity on particle
\(u_g\): velocity on grid
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PIC
approach - Transfert velocity from grid to particles
\(u_p^{k+1}=interp(u_g^{k+1},p^{k+1})\)
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FLIP
approach - Add velocity difference from grid to particles.
\(u_p^{k+1}=v_p^k+(interp(u_g^{k+1}, p^{k+1})-interp(u_g^{k},p^{k}))\)
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PIC/FLIP
: blending b/w two approaches
Y. Zhu and R. Bridson, Animating Sand as a Fluid, ACM SIGGRAPH 2005
PIC: Stable, smoothed-out
FLIP: Details, few dissipation
