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

With a view to simulating the entire process of a landslide-triggered tsunami, ranging from tsunami generation to offshore wave propagation, with relatively low computational costs, we present a 2D–3D coupling strategy to bridge 3D MPM–FEM hybrid and 2D shallow water (SW) simulations. Specifically, considering the difference in basis functions between the 3D and 2D analysis methods, we devise a novel variable passing scheme in the domain overlapping method, in which a slightly overlapped domain enables the generated wave to pass through the connection boundaries with as little discrepancy as possible. For the tsunami generation stage in the 3D domain, the hybrid method combining the finite element method (FEM) and material point method (MPM) is adopted. In this method, the 3D governing equation of the solid phase is solved with the MPM, whereas the well-established 3D stabilized FEM is applied to that of the fluid phase in an Eulerian frame. Additionally, the phase-field method is employed to track the free surface of the 3D fluid domain. On the other hand, the SW equation that represents the offshore wave motion in the 2D domain is solved by the 2D stabilized FEM. Several numerical examples are presented to demonstrate the effectiveness of the developed scheme in properly passing the data from 3D/2D to 2D/3D domains.