Free-surface flows, especially those associated with fluid-structure interactions (FSIs), pose challenging problems in numerical simulations. The authors of this work recently developed a smoothed particle element method (SPEM) to simulate FSIs. In this method, both the fluid and solid regions are initially modeled using a smoothed finite element method (S-FEM) in a Lagrangian frame, whereas the fluid regions undergoing large deformations are adaptively converted into particles and modeled with an improved smoothed particle hydrodynamics (SPH) method. This approach greatly improves computational accuracy and efficiency because of the advantages of the S-FEM in efficiently treating solid/fluid regions showing small deformations and the SPH method in effectively modeling moving interfaces. In this work, we further enhance the efficiency of the SPEM while effectively capturing local fluid information by introducing a multi-resolution technique to the SPEM and developing an effective approach to treat multi-resolution element-particle interfaces. Various numerical examples demonstrate that the multiresolution SPEM can significantly reduce the computational cost relative to the original version with a constant resolution. Moreover, the novel approach is effective in modeling various incompressible flow problems involving FSIs.

自由表面流动，尤其是与流固耦合 (FSI) 相关的流动，在数值模拟中提出了具有挑战性的问题。这项工作的作者最近开发了一种平滑粒子元素方法 (SPEM) 来模拟 FSI。在这种方法中，流体和固体区域最初都使用拉格朗日框架中的平滑有限元方法 (S-FEM) 进行建模，而经历大变形的流体区域则自适应地转换为粒子并使用改进的平滑粒子流体动力学进行建模（ SPH) 方法。由于 S-FEM 在有效处理显示小变形的固体/流体区域和 SPH 方法在有效建模移动界面方面的优势，这种方法大大提高了计算精度和效率。在这项工作中，我们通过将多分辨率技术引入 SPEM 并开发处理多分辨率元素-粒子界面的有效方法，进一步提高了 SPEM 的效率，同时有效地捕获了局部流体信息。各种数值示例表明，相对于具有恒定分辨率的原始版本，多分辨率 SPEM 可以显着降低计算成本。此外，这种新颖的方法可以有效地模拟涉及 FSI 的各种不可压缩流动问题。各种数值示例表明，相对于具有恒定分辨率的原始版本，多分辨率 SPEM 可以显着降低计算成本。此外，这种新颖的方法可以有效地模拟涉及 FSI 的各种不可压缩流动问题。各种数值示例表明，相对于具有恒定分辨率的原始版本，多分辨率 SPEM 可以显着降低计算成本。此外，这种新颖的方法可以有效地模拟涉及 FSI 的各种不可压缩流动问题。