Liquid sloshing flows interacting with deformable structures are difficult to be numerically simulated due to the co-existence of moving fluid-structure interfaces and breaking free surfaces. As a Lagrangian and particle-based method, the smoothed particle hydrodynamics (SPH) method has natural advantages in handling free-surface flows. The smoothed finite element method (SFEM) provides a reliable tool to capture the associated structural deformations, and it can solve the “overly-stiff” problem in the conventional FEM. In this work, the coupling strategy of an improved SPH version and SFEM is integrated with advanced fluid modeling techniques, and is extended and validated for modeling liquid sloshing with rigid or deformable structures. Both the rigid wall boundaries and deformable structures are reproduced by the elements, whereas the fluid particles with a different resolution can be adopted. The integrated δ-SPH model can significantly alleviate the spurious high-frequency noise of the computed impact pressure in a sloshing process. The particle shifting technique helps improve both accuracy and robustness of the fluid flow model. The virtual particle coupling strategy is effective to transfer information between SPH particles and SFEM elements. Various numerical tests show that the present coupling approach is very effective for modeling violent sloshing with deformable baffles or deformable container walls. This method is more accurate than the conventional coupling of SPH-FEM and can obtain results very close to the experimental observations compared with some numerical approaches from other sources.

由于移动的流固界面和断裂自由表面的共存，与可变形结构相互作用的液体晃荡流难以进行数值模拟。作为拉格朗日和基于粒子的方法，平滑粒子流体动力学 (SPH) 方法在处理自由表面流动方面具有天然优势。平滑有限元法 (SFEM) 提供了一种可靠的工具来捕捉相关的结构变形，它可以解决传统 FEM 中的“过硬”问题。在这项工作中，改进的 SPH 版本和 SFEM 的耦合策略与先进的流体建模技术相结合，并被扩展和验证用于建模具有刚性或可变形结构的液体晃动。刚性墙边界和可变形结构都由元素再现，而可以采用不同分辨率的流体粒子。集成的δ- SPH 模型可以显着减轻晃荡过程中计算的冲击压力的虚假高频噪声。粒子移动技术有助于提高流体流动模型的准确性和鲁棒性。虚拟粒子耦合策略可以有效地在 SPH 粒子和 SFEM 元素之间传递信息。各种数值试验表明，本耦合方法对于模拟具有可变形挡板或可变形容器壁的剧烈晃动非常有效。这种方法比传统的 SPH-FEM 耦合更准确，并且与来自其他来源的一些数值方法相比，可以获得非常接近实验观察的结果。