## 1 Introduction
The performed study showed that, at angles of attack between 60\({}^{\circ}\) and 80\({}^{\circ}\), vortex instability produces noticeable fluctuations in the lateral forces, with the peak-to-peak amplitude of cross-sectional lateral force coefficients reaching 2.0. [PERSON] et al. [10; 11] performed numerical simulations and experimental investigations on a high angle of attack and low Reynolds number flow over a hemispherical nose cylinder using DNS and discussed the mechanism of vortex shedding. Of course, there are many factors that affect the lateral force on an object at large attack angles in aerodynamics, such as surface roughness. [PERSON] [12] investigated turbulent flows past a rough circular cylinder under the moving wall effect in the large-gap regime, while [PERSON] [13] explored the influence mechanism of surface roughness on a cylinder vortex-induced vibration (VIV) by introducing the modified model of rough wall velocity gradient. At this stage in our research, we mainly focus on the force mechanism of submarines under large attack angles. Therefore, the calculation object and physical model assumed in this paper are both in a smooth state. Accurate capture of vortex shedding is a critical aspect of numerical calculations for a high angle of attack. The choice of the turbulence model and reasonable network design are two important factors. The detached eddy simulation (DES) represents a hybrid modeling method [14] that combines the advantages of Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES). The RANS methodology is commonly employed in the near-wall region to reduce the number of grids and computational resources, whereas the LES method is utilized in the far-wall region to effectively resolve the conflict between the calculation accuracy and the computational resources. Currently, it has been extensively implemented to analyze the relevant engineering-based problems. In 1997, [PERSON] et al. [15] proposed the SA-DES model based on the Spalart-Allmaras (SA) model. Subsequently, researchers gradually improved it and proposed the delayed discrete eddy simulation (DDES) model and the improved one (IDDES). In this regard, [PERSON] and [PERSON] [16] utilized the DES model to simulate the flow around tandem circular cylinders. Using the DES model, [PERSON] and [PERSON] [17] studied the vibration problem caused by the vortex of a cylinder at different speeds and mass ratios. [PERSON] et al. [18] conducted a comparative study of the flow around a cylinder via the DDES approach and constrained LES models. Although the results of the constrained LES model were slightly better, its complexity was higher than that of the DDES model. [PERSON] [19] compared different RANS and DDES models, simulated the static flow and forced oscillation of the NACA0015 airfoil at high angles of attack, and compared the results with experimental values. The obtained results revealed that the SST-DDES model is effectively capable of capturing the vortex shedding on the leeward side of the airfoil and the obtained unsteady aerodynamic loads were in reasonably good agreement with the experimental values, whereas the RANS methods did not perform well. In numerical simulations, a proper mesh layout is another factor for accurate calculations, and adaptive mesh refinement (AMR) technology is an effective approach to adjust the accuracy of the solution in specific sensitive or turbulent simulation regions during the dynamic calculation process. AMR technology is capable of refining the mesh in certain regions during the numerical simulation process, leading to more accurate solution results. Currently, this technology has been increasingly adopted [20; 21; 22], but it requires reasonable adaptation criteria. [PERSON] et al. [23] developed an LES refinement criterion that represents the ratio of modeled kinetic energy based on the basic hypothesis of the LES. This approach uses the LES simulation results to estimate the appropriate length scale of the LES grid for automatic refinement, arriving at better results.