A new method for material point method particle updates that reduces noise and enhances stability.

Current material point method (MPM) particle updates use a PIC approach, a FLIP approach, or a linear combination of PIC and FLIP. A PIC update filters velocity in each time step, which causes unwanted numerical diffusion, while FLIP eliminates that diffusion, but may retain too much noise. This paper develops a new particle update termed XPIC( m ) (for eXtended PIC of order m ) because it generalizes PIC updates. XPIC(1) is identical to current PIC methods, but higher orders of XPIC( m ) address the over filtering and numerical diffusion of PIC, while still filtering out noise caused by the nontrivial null space of the extrapolation matrix used in MPM. As m → ∞ , XPIC( m ) converges to a modified FLIP update with orthogonal removal of null space noise. The frequency response and filtering properties of XPIC( m ) are investigated and several numerical examples demonstrate its advantages over other update methods. [ABSTRACT FROM AUTHOR]