###### Abstract
[PERSON] and [PERSON] [15] performed the numerical simulations of a near-wall cylinder with small gap ratios (\(e/D\leq 0.5\)) at \(Re=200\) and they found that the largest amplitude and the natural frequency of the cylinder and the vortex shedding from the cylinder are significantly affected by the wall. [PERSON] and [PERSON] [16] identified C (chaotic), P (periodic), and QP (quasi-periodic) vortex shedding modes at two \(e/D\) and mass ratios for a circular cylinder undergoing VIV near a solid wall. These studies of the VIV of a circular cylinder near a stationary wall can serve as a foundation to improve pipeline design guidelines [17]. In addition, many engineering structures are in arrays, such as bridge piers, groups of chimney stacks, bridge pier offshore platforms, etc. Unlike the single freely vibrated cylinder, the vibration of a cylinder in a tandem-arrangement system is affected not only by its own vortex shedding but also by the vortex generated by the adjacent cylinder [18]. Figure 1: Examples of near-wall cylindrical structures in engineering practices. (**a,b**): deep-water pipeline system; (**c**): flat-bottomed ground-supported silos. [PERSON] [19] classified the flows around two tandem free-wall cylinders into three regimes, i.e., the extended-body regime (\(1<L/D<1.5\), with \(L\) being the center to center space of two cylinders), reattachment regime (\(1.5<L/D<4\)), and co-shedding regime (\(L/D>4\)). In an extended-body regime, the free shear layers separated from the upstream cylinder overshoot the downstream ones. In the reattachment regime, the upstream separated shear layers reattach to the downstream cylinder. In the co-shedding regime, the shear layers roll up alternatively and form a vortex street in the gap between as well as behind the cylinders. The reattachment regime is further divided by [PERSON] et al. [20] into two regimes based on the lift force coefficients on the cylinders: the alternating reattachment regime (\(1.5<L/D<3\)) and steady reattachment regime (\(3<L/D<4\)). To the best of the authors' knowledge, few studies have investigated the VIV of two cylinders in a tandem arrangement close to a stationary wall, although it is highly relevant to many engineering practices, such as the free-spanning vibration of two parallel pipelines close to the sea bed. [PERSON] et al. [21] investigated the VIV of two inline circular cylinders near a stationary wall at \(Re=100\) and \(m^{*}=2\). In their work, the features of vibration amplitudes, frequencies, wake patterns, fluid forces, position shifts, and vibration trajectories are explored for two gap ratios. This paper aims to investigate the differences between the VIV of a cylinder and two inline cylinders near a plane wall. In particular, the collision of the cylinder and the plane wall is considered and the cylinders can only oscillate in the transverse direction. This work can be regarded as a supplement and validation for the previous studies. The VIV of a circular cylinder is a typical fluid-structure interaction (FSI) problem and the numerical methods can be divided into a body-fitted grid and a non-body-fitted grid. In body-fitted-grid methods, the mesh quality and computational efficiency cannot be guaranteed when the gap ratio is small. The immersed boundary (IB) method is one of the non-body-fitted-grid methods that is commonly used for solving moving-boundary problems to avoid the application of a remeshing technique. [PERSON] et al. [22] proposed an IB method, called the local domain-free discretization (DFD) method, in which the discrete forces that represent the wall effects are implicitly applied to the discretized Navier-Stokes (N-S) equations. In the local DFD method, some exterior nodes may be involved in the discrete form of the governing equations at a near-wall interior node. The functional solutions at these exterior dependent nodes are reconstructed by a proper local extrapolation with boundary conditions imposed.