Development of stabilized mixed material point method for incompressible fluid flow analysis: formulation and validation

Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Kenneth Kamrin, Kenichi Soga

Keywords: Material point method, Incompressible fluid, Implicit time integration, Stabilized methods, Mixed formulation

Abstract: Simulation of incompressible fluid flow using the material point method (MPM) confronts significant challenges stemming from three key issues: (i) volumetric locking due to the incompressibility constraint, (ii) the accumulation of quadrature errors, and (iii) instabilities induced by the transfer of information between particles and background grids. To address these issues, the current research develops a novel and robust stabilized formulation of MPM aimed at accurately modeling incompressible fluid flow. In addressing the modeling of Newtonian fluids with incompressibility constraints, a novel fully-implicit mixed formulation of MPM for free-surface flow is proposed. Diverging from conventional practices of treating velocity and pressure fields as unknown variables in typical Eulerian computational fluid dynamics (CFD) solvers, our approach adopts a monolithic displacement-pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). By coupling the displacement and pressure fields and solving them monolithically, the developed solver eliminates the need for free-surface pressure detection and imposition, distinguishing it from the typical fractional-step method. This attribute effectively mitigates spurious pressure oscillations that often arise from toggling free-surface nodal pressure imposition on and off, as the fluid front moves through the background grid. The effectiveness of the proposed stabilized incompressible MPM has been validated through extensive comparisons with other numerical methods across a variety of benchmark cases. Moreover, the method's capability in simulating real-world scenarios involving violent free-surface fluid motion is demonstrated through comparisons with experimental results from water sloshing and dam break scenarios.

Submission Number: 6