# Investigation on Numerical Simulation of VIV of Deep-Sea Flexible Risers
## 1 Introduction
The numerical simulation method has become an indispensable complement to experiments in ocean engineering [16]. With improvement in computing efficiency, the VIV study of long flexible risers using numerical models has become increasingly common. However, with the increase in the riser slenderness ratio, three-dimensional numerical simulation has become increasingly difficult. Therefore, numerical simulation of risers' VIV coupled with a two-dimensional fluid and three-dimensional structure based on the slice method has attracted the attention of researchers. In 2004, [PERSON]. [17] adopted the discrete vortex method (DVM) to establish a quasi-three-dimensional riser vortex-induced vibration model and solved the structural part of the dynamic equation according to the Euler-Bernoulli beam theory. The numerical simulation results of flexible riser VIV at different flow velocities were compared with the experimental results, and it was observed that the wake vortex shedding mode was 2P for the riser with a larger amplitude and 2S for the riser with a smaller amplitude. [PERSON] and [PERSON] [18] used the Lattice Spring Method (LSM) combined with the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to investigate fluid-elastic body interaction problems in unsteady conditions. The LSM needs no arbitrary spring parameters to determine the deformation of the flexible body. [PERSON] and [PERSON] [19] combined the RANS method and finite element method to solve the structural dynamic response, divided the response into multiple slices to establish a quasi-three-dimensional model, and carried out VIV numerical simulation research on a flexible riser under shear flow. The researchers used this method to analyze the VIV response of the top tension riser. [PERSON] et al. [20; 21; 22; 23] developed a computational fluid dynamics (CFD) solver, VIV FOAM SJTU, on the Open FOAM platform based on the slice method, and amplitudes of the risers in the IL and CF directions were accurately predicted. In 2020, [PERSON] [24], based on the Fluent solver and a self-compiled UDF, carried out numerical simulation research on a three-dimensional flexible riser vortex-induced vibration under different flow speeds and demonstrated the phenomenon of the adjacent order vibration mode switching of the flexible riser vortex-induced vibration with a change in flow velocity. The phenomena of the \"traveling wave\" and \"standing wave\" of the flexible riser were observed. At the same time, the frequency of the VIV response of a flexible riser was analyzed, and the phenomenon of multi-frequency vibration was observed. In particular, it was found that the vortex-induced vibration characteristics of the riser showed a vibration response with a wide-band spectrum when the inflow velocity was relatively high. In this paper, we accurately predict the fatigue damage of deep-sea flexible risers, and numerical analysis methods based on the slicing method offer valuable insights into the dynamic response of vortex-induced vibration. Using a self-compiled UDF program and overset mesh technique to reveal the nonlinear dynamic features of flexible riser vibration, our research focuses on further improving these numerical simulation methods to provide more accurate and reliable predictions of fatigue damage in deep-sea flexible risers.