## 3 Numerical Simulation
### Mesh Generation  
Due to the complex geometry of the rearview mirror, a triangular surface mesh can simulate the complex 3D model more accurately than other meshes [19], so a triangular surface mesh was used for the flow field calculation. In order to ensure the accuracy of the model, the surface mesh was encrypted at the mirrors with a mesh size of 1 mm, the mesh size of the rest of the body was 1-16 mm, and the mesh size of the computational domain was 512 mm. In order to ensure that the Y+ value met the requirements (Y+ \(<\) 1) of the large eddy simulation (LES), the volumetric mesh was generated with eight layers of prisms, with a prism layer extension of 1.5, and the total thickness of the prism layers was 0.6 mm. The cloud of Y+ values on the surface of the rearview mirror is shown in Figure 3. Meanwhile, in order to correctly capture the flow information around the vehicle model, three encrypted domains were set up around the model, with sizes of 16 mm, 64 mm, and 128 mm, respectively. The final mesh size was 32 million. The mesh profile is shown in Figure 4.  
Figure 1: Simplified vehicle model.  
Figure 2: Computational domain.  
Large eddy simulation divides turbulence into eddies of different sizes. Where larger scale eddies are solved by direct numerical simulation and smaller scale eddies are solved by a generic model, large eddy simulation can simulate turbulent flow well. There are two important aspects to realizing a large eddy simulation:  
1. The development of a mathematical filtering model to decompose the equations describing large eddies by filtering out eddies with scales smaller than the scale of the filter function from the turbulent instantaneous equations of motion.
2. Considering the effect of the filtered out small eddies on the large eddies. This is captured by introducing an additional stress term in the equations of motion for the large vortex flow field, which is referred to as subgrid-scale stress. This mathematical model is called the subgrid-scale model (SGS model).  
The N-S equation for the instantaneous state and the continuum equation are handled by the filter function:  
\[\frac{\partial}{\partial t}(\rho\overline{u}_{i})+\frac{\partial}{\partial x_{ j}}\big{(}\rho\overline{u}\overline{u}_{j}\big{)}=-\frac{\partial\overline{p}}{ \partial x_{i}}+\frac{\partial}{\partial x_{j}}\left(\mu\frac{\partial\overline {u}_{i}}{\partial x_{j}}\right)-\frac{\partial\tau_{ij}}{\partial x_{j}} \tag{13}\]  
\[\frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x_{i}}(\rho\overline {u}_{i})=0 \tag{14}\]  
The two equations above are the set of control equations used for the large eddy simulation, with the quantities with an overline being the filtered field variables.  
Figure 4: Mesh along the symmetry plane.  
Figure 3: Y+ value of rearview mirror surface.  
is a subgrid scale stress. The force reflects the effect of small-scale vortex motion on the solved equations of motion.  
A commonly used subgrid model is the Smargorinsky model. Assuming that the small-scale pulsations filtered out with isotropic filters are locally balanced, i.e., the energy transfer from the solvable scale terms of the unsolvable scale pulsations is equal to the turbulent energy dissipation, [PERSON]'s sublattice Reynolds stress model can be used:  
\[\overline{\tau}_{ij}=\left(\overline{u_{i}u_{j}}-\overline{u_{i}u_{j}}\right)= 2(C_{s}\Delta)^{2}\overline{S}_{ij}\left(\overline{S}_{ij}\overline{S}_{ij} \right)^{1/2}-\frac{1}{3}\overline{\tau}_{kk}\delta_{ij} \tag{15}\]  
where \(\Delta\) is the filtering scale. This simple sub-lattice stress model is called the Smargorinsky model. Sublattice vortex viscosity factor \(v_{t}=\left(C_{s}\Delta\right)^{2}\left(\overline{S}_{ij}\overline{S}_{ij} \right)^{1/2}\); \(C_{s}\Delta\) is the mixing length; \(C_{s}\) is the Smagorinsky constant; \(C_{s}=0.18\).