## 2 Models and Methods
### Numerical Model
#### 2.2.3 Boundary Conditions  
A finite-difference approximation requires defining a solution at the domain boundaries to receive a unique solution. This case is an example of airflow around a vehicle model in a channel. In order to avoid interaction of the airflow structures caused by the [PERSON] body shape with channel planes, it is necessary to ensure the appropriate size of the computational domain. For this purpose, a \(1\L\times 2\L\times 8\L\) calculation area was created around the [PERSON] body geometry, where L is the vehicle's characteristic length of 1.044 m. The major turbulence and swirl structures of the airflow are observed in the wake behind the vehicle. This area is defined as five vehicle lengths in the x-coordinate. Because of a high pressure area at the front of the vehicle model, the distance between inlet plane and [PERSON] body surface is defined as two characteristic lengths. Similar recommendations on the size of the computational domain are used by the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC). The computational domain with surfaces names is presented in Figure 3. The no-slip condition was applied to the surface of the [PERSON] body (Surface G) and bottom plane (Surface A). The front plane (Surface B), where the fluid enters the computational area, was selected as the inlet boundary condition. Depending on the simulation, air velocity was in range from 20 to 100 m/s. The pressure gradient was zero for this surface. The outlet boundary condition was employed on the plane where the air leaves the flow field (Surface E). A reference pressure of zero was assumed. Zero gradients were applied for other parameters. A symmetry condition was applied along the middle section of the body for plane \(y=0\) (Surface F). This results in reducing the number of elements and increasing the speed of calculations. The boundary condition with the coordinates of each surface are described in detail in Equations (19)-(44). (Surface A) The bottom surface of the channel is defined as a stationary wall with a no-slip condition:  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]  
\[\frac{\partial k}{\partial z}=0,\quad\frac{\partial\omega}{\partial z}=0, \quad\
abla p=0 \tag{20}\]  
\[k_{w}=\frac{u_{\tau}^{2}}{\sqrt{\beta_{\rm so}^{*}}} \tag{21}\]  
Figure 3: Surface description for boundary conditions. \[\omega_{w}=\frac{u_{\tau}}{\kappa y_{w}\sqrt{\beta_{\infty}^{*}}} \tag{22}\]  
\[\text{for}\quad-3.132m\leq x\leq 5.22m,\quad 0\leq y\leq 1.044m,\quad z=0\]  
where:  
\(k_{w}\)--turbulent kinetic energy in the wall cell  
\(\omega_{w}\)--specific turbulence dissipation in the wall cell  
\(y_{w}\)--distance from wall to cell centroid. (Surface B) At the inlet of the channel the air velocity is fixed to a constant value. Depending on the case the velocity is from 20 to 100 m/s:  
(a) Studies of pressure and velocity distribution, streamlines in symmetry plane \(y=0\), comparison of vortex system (Section 3.1), streamwise velocity profiles, drag and lift coefficient as a function of time (Section 3.2), overall sound pressure level and A-weighting sound pressure level (Section 3.4):  
\[u_{x}=40\frac{m}{s},\quad u_{y}=0,\quad u_{z}=0 \tag{23}\]  
\[\
abla p=0 \tag{24}\]  
\[k=\frac{3}{2}(u_{x}I)^{2} \tag{25}\]  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]0  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]1  
where:  
\(I=1\%\)  
\(\frac{\mu_{t}}{\mu_{p}}=10\)  
(b) Investigation of drag coefficient as a function of the Reynolds number (Section 3.3):  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]2  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]3  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]4  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]5  
\[u_{x}=0,\quad u_{y}=0,\quad u_{z}=0 \tag{19}\]6  
where:  
\(I=1\%\)--turbulence intensity  
\(\frac{\mu_{t}}{\mu_{p}}=10\)--turbulent viscosity ratio.