As a mesh-free method, smoothed particle hydrodynamics (SPH) has been widely used for modeling and simulating fluid-structure interaction (FSI) problems. While the kernel gradient correction (KGC) method is commonly applied in structural domains to enhance numerical consistency, high-order consistency corrections that preserve conservation remain underutilized in fluid domains despite their critical role in FSI analysis, especially for the multi-resolution scheme where fluid domains generally have a low resolution. In this study, we incorporate the reverse kernel gradient correction (RKGC) formulation, a conservative high-order consistency approximation, into the fluid discretization for solving FSI problems. RKGC has been proven to achieve exact second-order convergence with relaxed particles and improve numerical accuracy while particularly enhancing energy conservation in free-surface flow simulations. By integrating this correction into the Riemann SPH method to solve different typical FSI problems with a multi-resolution scheme, numerical results consistently show improvements in accuracy and convergence compared to uncorrected fluid discretization. Despite these advances, further refinement of correction techniques for solid domains and fluid-structure interfaces remains significant for enhancing the overall accuracy of SPH-based FSI modeling and simulation.

翻译：作为一种无网格方法，光滑粒子流体动力学（SPH）已被广泛应用于流固耦合（FSI）问题的建模与仿真。尽管核函数梯度修正（KGC）方法在结构域中常被用于增强数值一致性，但在流体域中，能够保持守恒性的高阶一致性修正方法仍未得到充分利用，尽管其在FSI分析中具有关键作用，尤其是在流体域通常分辨率较低的多分辨率方案中。本研究将反向核函数梯度修正（RKGC）公式——一种守恒的高阶一致性近似方法——引入流体离散化过程以求解FSI问题。RKGC已被证明能够在粒子分布松弛的情况下实现精确的二阶收敛，提高数值精度，并尤其在自由表面流动模拟中显著增强能量守恒性。通过将该修正方法整合到黎曼SPH方法中，采用多分辨率方案求解不同典型FSI问题，数值结果一致表明，相较于未修正的流体离散化方法，其精度和收敛性均得到改善。尽管取得了这些进展，针对固体域及流固界面的修正技术仍需进一步优化，这对于提升基于SPH的FSI建模与仿真的整体精度具有重要意义。