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.