High-order parametric curve reconstruction method for surface mesh mapping in vortex-induced vibrations of slender catenary structures

Slender catenary flexible structures, such as free-span submarine cables, exhibit pronounced geometric nonlinearity and complex multi-modal vortex-induced vibration (VIV) responses, presenting a considerable challenge for high-fidelity fluid-structure interaction (FSI) simulations. Conventional mesh mapping techniques often struggle to concurrently ensure geometric accuracy and physical consistency for such curved interfaces undergoing large deformations. This paper presents a surface mesh mapping method based on high-order parametric spatial curve reconstruction is constructed. The proposed method implements two key improvements: firstly, discrete nodal displacements obtained from a one-dimensional structural model are reconstructed into smooth and spatially analytic curves via a global high-order polynomial fitting technique; secondly, permanent geometric associations between each mesh point in the fluid domain and a reference point on the structural central axis is established. By incorporating these procedures, a rigorous analytical mapping framework is established, which accurately and consistently transfers 1D structural deformations to the 3D fluid mesh. Building upon this method, a high-fidelity FSI solver for predicting VIV responses of slender catenary structures is developed within OpenFOAM. The effectiveness of the solver is validated against systematic model tests conducted on a free-span submarine cable under both free decay and uniform-flow conditions. Numerical results demonstrate excellent agreement with experimental data in various aspects including natural frequencies, multi-modal evolution patterns, and complex in-line/cross-flow coupled vibration characteristics. Compared to traditional low-order interpolation approaches, the proposed method shows marked advantages in geometric smoothness, interface motion consistency, and long-term numerical stability. It thus provides a reliable and high-fidelity numerical tool for the accurate prediction of VIV responses of offshore catenary structures.