A stabilized fractional-step MPM with pressure gradient projection for coupled hydromechanical extreme deformations

Le résumé fourni par la source

We present a novel stabilized fractional-step two-phase double-point Material Point Method (MPM) for robust and computationally efficient simulations of extreme-deformation hydromechanical problems. Existing fractional-step models employ either a non-incremental pressure discretization, which is suitable for large deformations but inaccurate under low permeability conditions, or an incremental formulation that improves accuracy yet relies on stabilization methods that are currently inadequate for large deformations. To overcome these limitations, we present the first adaptation of the Stabilized Pressure by Gradient Projection (SPGP) method to the MPM framework and propose a Taylor Particle-in-Cell (TPIC) pressure mapping for improved free-surface treatment. A generalized temporal discretization for pressure and drag is developed, providing new insights into the numerical behavior of non-incremental and incremental fractional-step schemes. In particular, we demonstrate that the non-incremental formulation remains inherently sensitive to permeability, whereas the incremental formulation achieves superior accuracy with permeability-independent timesteps, eliminating the need for complex drag discretizations. The proposed method is implemented in the high-performance Taichi programming language, leveraging GPU acceleration and sparse grid capabilities, combined with a matrix-free conjugate gradient algorithm to efficiently solve the pressure-Poisson system. Our model is validated against a series of benchmark problems covering large deformations and phase separation phenomena, demonstrating high accuracy and robustness without case-specific tuning of stabilization parameters. This advancement establishes a unified and robust foundation for simulating coupled hydromechanical processes, such as water-rich geophysical mass flows.

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