MPM–FEM hybrid method for granular mass–water interaction problems

Abstract

The present study proposes an MPM (material point method)–FEM (finite element method) hybrid analysis method for simulating granular mass–water interaction problems, in which the granular mass causes dynamic motion of the surrounding water. While the MPM is applied to the solid (soil) phase whose motion is suitably represented by Lagrangian description, the FEM is applied to the fluid (water) phase that is adapted for Eulerian description. Also, the phase-field approach is employed to capture the free surface. After the accuracy of the proposed method is tested by comparing the results to some analytical solutions of the consolidation theory, several numerical examples are presented to demonstrate its capability in simulating fluid motions induced by granular mass movements.

Variable passing method for combining 3D MPM–FEM hybrid and 2D shallow water simulations of landslide‐induced tsunamis

“…We employ the MPM–FEM hybrid method 16 to generate 3D landslide‐induced tsunamis, in which the MPM with the Lagrangian description is applied to discretize the governing equations of the solid skeleton, whereas the stabilized FEM with the SUPG/PSPG stabilization scheme 28,37 with the Eulerian description is applied for those of the fluid phase. Although linear tetrahedral elements were used by Ling et al 26,27 to address fluid flow only in the 3D domain, $$$ {\varOmega}^{3\mathrm{D}} $$$, regular hexahedron cells with quadratic B‐spline basis functions are used to suppress the cell‐crossing error that often arises when using the MPM with C$$$ {}^0 $$$‐continuous basis functions 38,39 .…”

“…We employ different $$$ \Theta $$$ depending on the governing equations. For the solid phase, we solve the nodal acceleration explicitly with $$$ \Theta =0 $$$, while the nodal solutions of the fluid phase, where the SW equation and the Allen–Cahn equation are given, are solved implicitly with $$$ \Theta =0.5 $$$ (the so‐called Crank–Nicolson method); see Pan et al 16 for more details.…”

“…To examine the capability and efficiency of the proposed method in reproducing a comparative result with the full 3D simulation by the MPM–FEM hybrid scheme, 16 we target the laboratory experiment 43 in a water tank mimicking a subaerial landslide‐induced wave.…”

“…Among them, the fractional‐step method 15 is the most popular method for accommodating the incompressibility of the liquid phase in a solid–liquid mixture; see, for example, References 10 and 12, to name a few. Another approach worth mentioning is the MPM–FEM hybrid method, 16 in which the MPM for the solid phase is coupled with the stabilized FEM for incompressible fluids; this approach appears promising for the target problem because of its characteristic feature in dealing with the solid and fluid phases separately.…”

“…Indeed, the original domain overlapping method by Ling et al 26,27 only considers fluid flow and therefore uses the same low-order interpolation function for the 2D and 3D domains. However, the MPM-FEM hybrid method 16 commonly uses high-order B-spline basis functions for both fluid and solid motions to suppress the cell-crossing error that often arises when using the MPM with low-order basis functions, while low-order interpolation is adopted for 2D SW simulations. Thus, the existing 2D-3D FEM cannot be applied as is unless the difference in interpolation orders is taken into account when passing variables.…”