## 2 Simulation of 3D Ship Airwake by CFD  
### Numerical Model of Aircraft Carrier  
The software and processes used in the CFD simulation in this article are as follows:  
1. The Solidworks (2022) software was used to draw the geometric model of the ship; ANSYS (2021 R1) Spacedaim software was used to improve the geometric model of the ship and draw the computational domain; and ANSYS (2021 R1) Fluent Meshing software was used to perform meshing on the physical model;
2. When using ANSYS (2021 R1) Fluent Solution software to generate the simulation model, various solution parameters need to be set, such as turbulence models, boundary conditions, solvers, equation discretization formats, and solution algorithms;
3. Using ANSYS (2021 R1) CFD-POST software for post-processing of the solution results, we can extract and analyze the 3D ship airwake on the glide path.  
The conceptual design of the aircraft carrier model adopts a coordinate system with the x-axis along the stern direction, the y-axis along the starboard side, and the z-axis perpendicular to the deck pointing upward, as shown in Figure 2. The computational domain uses a cuboid solid region with a length of 952 m, approximately three times the length of the aircraft carrier (294 m). The width of the domain is 398 m, about four times the width of the ship (96 m), and its height is 216 m, about three times the height of the ship (65 m, above the waterline). The influence of ocean waves is negligible, assuming the ship moves steadily along a specific course with a constant draft, and the sea surface is treated as a horizontal solid wall. The inflow boundary of the domain adopts a velocity inlet, while the outflow boundary employs a pressure outlet. Global meshing employs Poly-Hexcore grids (a combination of polyhedral and Cartesian grids), which provide higher filling efficiency and higher grid quality, while grid refinement is applied to the adjacent region and the ship aft glide path region, as shown in Figure 3. The boundary layer number is set to 5, and its cell quality limit value is set to 0.15. The total cell count is approximately 16 million, with a minimum cell size of about 0.88 m.  
Considering the carrier speed and sea surface wind conditions, the typical wind speed over the deck ranges from 0 to 40 m/s. Due to the low Mach number, the ship airwake is treated as incompressible. The simulation excludes the effects of exhaust emissions from the shipboard engines and chimney, as well as heat exchange between the ship and the surrounding air. To verify that the ship airwake structure calculated by steady CFD calculation is accurate, we carried out ship airwake simulation with a transient turbulence model and a steady turbulence model. For steady Reynolds-averaged Navier-Stokes(RANS) calculations, the standard k-\(\varepsilon\) turbulence model is adopted, while the unsteady detached eddy simulation (DES) calculations use the k-\(\omega\) SST turbulence model. In the DES-SST model, unsteady simulations are performed with a residual convergence threshold of 0.001, a total of 1000 time-steps, and a time-step size of 0.05 s. The calculation is based on the pressure solver, primarily because it is suitable for incompressible fluids and requires less calculation. The SIMPLE algorithm is used for the pressure-velocity coupling term in the momentum equations, while the bounded central differencing scheme is applied for discretizing the momentum equations. Turbulent viscosity is discretized using a second-order upwind scheme, pressure equations are discretized with second-order spatial accuracy, and the temporal terms employ a bounded second-order implicit scheme. The airflow field around the aircraft carrier is shown in Figure 4.  
Figure 4: Airflow field around the aircraft carrier: streamlines (**left**) and contours (**right**).  
Figure 3: Surface mesh (**left**) and internal mesh (**right**).  
Figure 2: Models of the aircraft carrier and computational domain.