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.

中文翻译：

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结合滑坡诱发海啸的 3D MPM-FEM 混合和 2D 浅水模拟的变量传递方法

为了以相对较低的计算成本模拟滑坡引发的海啸的整个过程，从海啸产生到近海波浪传播，我们提出了一种 2D-3D 耦合策略来桥接 3D MPM-FEM 混合和 2D 浅水（ SW）模拟。具体来说，考虑到3D和2D分析方法之间基函数的差异，我们在域重叠方法中设计了一种新颖的变量传递方案，其中稍微重叠的域使得生成的波能够以最小的差异穿过连接边界可能的。对于3D域的海啸发生阶段，采用有限元法（FEM）和质点法（MPM）相结合的混合方法。在该方法中，固相的 3D 控制方程用 MPM 求解，而成熟的 3D 稳定有限元则应用于欧拉框架中的流体相。此外，还采用相场方法来跟踪 3D 流体域的自由表面。另一方面，表示二维域中近海波浪运动的 SW 方程由二维稳定有限元法求解。给出了几个数值示例来证明所开发方案在将数据从 3D/2D 域正确传递到 2D/3D 域方面的有效性。