Researchers have developed innovative stabilization strategies for modeling incompressible fluid flow using the Material Point Method (MPM). The proposed mixed implicit MPM formulation employs a monolithic displacement–pressure approach inspired by Finite Element Methods (FEM), bypassing the need for free-surface detection and pressure imposition. To enhance stability, the method integrates variational multiscale (VMS) and pressure-stabilization Petrov–Galerkin (PSPG) techniques, effectively reducing pressure and velocity oscillations. Additional improvements include quadratic B-Splines, delta-correction, and Taylor particle-in-cell methods to tackle common MPM challenges like cell-crossing errors. Validated through benchmark cases and experiments on water sloshing and dam breaks, this framework offers a robust tool for dynamic and transient flow problems.
Figure 1. Rotating square patch: evolution of pressure field at different time snapshots, obtained by the fractional-step and monolithic (unstabilized, PSPG, and VMS) approaches with FLIP scheme
Stabilized mixed material point method for incompressible fluid flow analysis
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga