Corrected Riemann smoothed particle hydrodynamics method for multi-resolution fluid–structure interaction

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 the fluid and solid domains are discretized with different spatial resolutions, along with the fluid domain generally having a lower resolution. In this study, we incorporate the reverse KGC (RKGC) formulation, a conservative correction approach in which KGC matrices are applied in reverse for each interacting particle pair to ensure high-order consistency in the approximations, 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. © 2025 Author(s).     «

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 the fluid and solid domain...     »