# Development of a Mobile Buoy with Controllable Wings: Design, Dynamics Analysis and Experiments
## 3 Fluid-Multibody Coupling Dynamics Model
### Hydrodynamics Model of the Mobile Buoy  
The computational domain and boundary conditions of the hydrodynamics model is shown in Figure 7a. The entire computational domain is a cube with \(10W\times 10W\times H\). The inlet surface is \(3W\) away from the model and is set as the velocity inlet, which was controlled by the UDFs based on Equation (13). The outlet surface is \(7W\) away from the model and set as the outflow boundary, which ensures the adequate development of vortex formation and shedding. The other boundary surfaces are set as non-slipping walls. Considering the heavy computational burden of the 3D flow field, the forward velocity of the mobile buoy, relative to the static fluid, transforms into the incoming flow that impacts the mobile buoy with the same velocity. Hence, the mobile buoy exclusively moves vertically and in pitch, while the forward motion is transformed into a non-constant incoming flow, enabling a reduction in the computational time required. The unstructured triangular meshes of the flow field are used, which can be seen in detail in Figure 7b. The surface mesh of the mobile buoy is shown in Figure 7c, and the zoom-in view shows the mesh of local area near the leading edge of the wing.  
Generally, the k-epsilon RNG turbulence model is more accurate and reliable in a broader range of flow scenarios. To ensure the computational accuracy, the k-epsilon RNG turbulence model and the transient and pressure-based solver are used for calculating. The SIMPLE scheme is used for solution method, the least squares cell-based scheme is used for gradient spatial discretization, and the second-order upwind scheme is applied for the spatial discretization of momentum, turbulent kinetic energy and turbulent dissipation rate. Three different types of grids are generated to verify the independence and reliability of the mesh model. All the three grids are of the same topology, only the number of mesh cells is different. The total number of cells for the coarse grid, the medium grid and the fine grid are 1,438,761, 2,375,926, and 4,798,272, respectively. The comparison of the instantaneous velocity and attitude variations during one motion cycle in Glider mode is shown in Figure 8. The data curves obtained from the three types of grids almost overlap, while the larger deviations only occur at the peaks and valleys. The data variations for different meshes exhibited a similar trend so that the calculation accuracy of three grids is similar. Generally, the fine grid with small sizes leads to high computational accuracy but imposes a heavy computational burden. Among the three grids, the medium grid exhibits a moderate computational accuracy, contributing to a reasonable computational burden. On the premise of ensuring accuracy, considering the computational efficiency of the medium  
Figure 7: The hydrodynamics model, showing **(a)** the 3D computational domain, **(b)** a zoom-in view of the flow field mesh in \(X\)-\(Y\) slice plane, **(c)** the surface mesh of the mobile buoy.  
grid is higher than the fine grid, the medium grid solution is adopted in the subsequent analysis to improve the computational efficiency.