# Investigation on Numerical Simulation of VIV of Deep-Sea Flexible Risers
## 1 Introduction  
Vortex-induced vibration (VIV) occurs due to the alternating shedding vortex formed by the instantaneous variable pressure difference on both sides of a structure. However, VIV increases the dynamic load of the structure [1] and can cause fatigue failure when subjected to long-term action. If deep-sea oil and gas pipelines suffer from fatigue damage and fracture, large amounts of oil and gas can leak into the ocean, causing serious environmental pollution and ecological disasters. Therefore, studying the dynamic response of VIV in deep-sea flexible risers is of great significance to accurately predict their fatigue damage. As early as 1981, [PERSON] et al. [2], a group of researchers in the United States, carried out VIV experiments of slender flexible risers using rising and falling tides. In 1997, [PERSON] et al. [3] carried out a VIV experiment of risers under shear flow on the west coast of Norway. In 2008, [PERSON] et al. [4] monitored the VIV characteristics of risers in the Gulf of Mexico within the water depth range of 360 m-2070 m.  
However, large-scale outdoor riser VIV experiments still have some shortcomings in the control of specific experimental parameters and data measurements. Therefore, researchers have begun to conduct indoor experimental research on the VIV of flexible risers in large water tanks. Professor [PERSON] and Professor [PERSON] [5] led a group of researchers to carry out a drag experiment focused on the VIV of a slender riser in a large water tank. The experimental results of the riser VIV response were compared with the predictions obtained by 11 different numerical methods (six CFD models and five empirical models), and it was found that the crossflow (CF) displacement predicted by the empirical models was more successful than that predicted by the CFD models. [PERSON] [6] conducted an experimentalstudy on the VIV of a flexible riser in a towing tank. The flow field profile demonstrated uniform flow, and the three-dimensional vibration response characteristics of the flexible riser were successfully captured. A VIV test of a flexible riser with a slenderness ratio of 481.5 was carried out by [PERSON] [7]. It was shown that (a) with an increase in flow velocity, the maximum displacement of the vortex-induced vibration of the riser increased; (b) the vibration frequency of the riser in the IL direction was twice that in the CF direction; and (c) the vibration modes excited in the CF direction reached up to the eighth order, while those excited in the IL direction reached up to the twelfth order. Since the length of a deep-sea flexible riser can reach 400-1500 m and operation in outdoor and laboratory tank tests is difficult, research on the VIV of deep-sea flexible risers using the numerical analysis method has attracted the attention of researchers. Numerical analysis methods for slender flexible risers are mainly divided into two categories: one is based on experimental data, such as empirical and semi-empirical models, and the other is the numerical simulation method based on computational fluid dynamics (CFD) and computational structural dynamics (CSD) [8]. Empirical and semi-empirical models need to be supported by massive experimental experiences, where the ranges of key parameters are given by fitting the experimental results. As early as 1964, [PERSON] and [PERSON] [9] proposed the [PERSON] wake oscillator model. [PERSON], [PERSON] and [PERSON] proposed a hybrid model that included an explicit Lattice Spring Model and an Immersed Boundary-non-Newtonian Lattice Boltzmann Method to simulate the behavior of filament in the vicinity of fluid flow. They also studied the effects of the fluid and structural characteristics on the motion of the filament and cylinder [10]. After more than half a century, an increasing number of empirical models have been proposed by scholars [11; 12; 13; 14; 15]. However, mode transition is an important feature of the VIV response of long flexible risers, but the empirical model cannot account for this switching process.