A high-performance semi-implicit two-phase two-layer MPM framework for modeling granular mass-water interaction problems

Most existing two-phase, two-layer Material Point Method (MPM) programs operate in explicit form, which lacks computational efficiency. This study proposes a high-performance semi-implicit two-phase two-layer MPM framework for modeling granular mass-water dynamic interaction problems based on mixture theory. This innovative approach employs two layers of material points and two layers of grids: a co-located grid dedicated to the solid phase and a Mark and Cell (MAC) staggered grid for the fluid phase. In this structure, the solid phase is solved explicitly, while the incompressible Navier-Stokes equations govern the fluid phase, utilizing a fractional-step method. To ensure the stability of the framework, the second-order B-spline basis function and the Affine Particle In Cell (APIC) mapping schemes are used for both phases. The proposed MPM is programmed using the Taichi language on the Graphics Processing Unit (GPU) platform, fully leveraging the data structures and parallel computing capabilities provided by Taichi to achieve efficient computation. Under the GPU framework, a parallel matrix-free preconditioned conjugate gradient (PCG) iteration is used to solve the pressure Poisson equation, overcoming the significant storage requirements caused by coefficient matrix assembly. Additionally, a geometric multigrid (MG) method is utilized for matrix preconditioning, achieving strong convergence and enabling efficient computation for large-scale linear systems. Furthermore, a prefix sum algorithm maintaining linear complexity in neighbor retrieval is innovatively proposed and implemented into DEM-based contact algorithm, enhancing calculation efficiency The comparisons with experimental data confirm the model's capacity to provide profound insights into granular mass-water interaction problems.