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

TL;DR

The paper addresses the challenge of accurately simulating fluid–structure interaction (FSI) when the fluid domain is coarsely resolved relative to solids in a multi-resolution SPH framework. It introduces a conservative high-order correction, the reverse kernel gradient correction (RKGC), into the fluid discretization of a Riemann-SPH formulation, incorporating a transport-velocity approach and WKGC weighting near free surfaces. The method is validated across hydrostatic, flow-induced vibration, dam-break, and sloshing benchmarks, showing improved accuracy, convergence, and energy conservation over standard SPH with multi-resolution. The findings support the viability of RKGC-corrected Riemann SPH as a robust, efficient tool for high-fidelity SPH-based FSI, with code available on GitHub to facilitate adoption and further development.

Abstract

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.

Figures (19)

• Figure 1: Hydrostatic water column on an elastic plate: Schematic illustration.
• Figure 2: Hydrostatic water column on an elastic plate: Distributions of fluid pressure and structural von Mises stress fields at $t = 0.5~\mathrm{s}$.
• Figure 3: Hydrostatic water column on an elastic plate: Time history of the vertical mid-span displacement of the elastic plate.
• Figure 4: Hydrostatic water column on an elastic plate: Time history of the normalized total energy for different methods.
• Figure 5: Flow-induced vibration of a beam behind a cylinder: Schematic illustrate. Sensor $M$ monitors the trajectory at the free end of the beam.