# CFD Assessment of Car Park Ventilation System in Case of Fire Event
## 2 Materials and Methods
### Discretization Process  
Figure 3 illustrates the utilization of Pointwise 18.2 software, which is a well-established and robust computational fluid dynamics (CFD) meshing tool renowned for its capability to generate high-quality and well-structured meshes [26]. The study implements a 3D structured mesh composed of hexahedral Cartesian elements. Despite the challenges inherent in dealing with large and complex geometries, the deliberate selection of a structured mesh over an unstructured alternative is motivated by a range of significant advantages, such as enhanced control and precision, improved convergence properties, access to supplementary solution algorithms, effective resolution of data locality issues, and the ability to define normal vectors [27]. A total of 173,332,000 nodes and 7,222,200 units were generated by the fluid grid division.  
In an OpenFOAM CFD simulation employing a Cartesian grid, a variety of parameters can be calculated using the finite volume method. This involves transforming the governing equations from their continuous formulation to integral forms across each volume, which includes the process of averaging the equations over the respective volume. These governing equations pertain to the discretization of partial differential equations (PDEs) within the Cartesian coordinate system, and the parameters under consideration encompass fundamental physical properties, such as velocity, pressure, temperature, and more. For incompressible flow without any source or sink terms, the corresponding continuous  
Figure 3: An enlarged portion of the mesh, providing improved resolution and detailed visualization.  
form of continuity equations (mass conservation--Equation (2)) and momentum equations (Navier-Stokes equations--Equation (3)) are as follows [28]:  
\[\frac{\partial\rho}{\partial t}+\frac{\partial(\rho u)}{\partial x}+\frac{ \partial(\rho v)}{\partial y}+\frac{\partial(\rho w)}{\partial z}=0 \tag{2}\]  
\[\frac{\partial(\rho u)}{\partial t}+\frac{\partial(\rho u)}{\partial x}+\frac{ \partial(\rho vu)}{\partial y}+\frac{\partial(\rho wu)}{\partial z}=-\frac{ \partial p}{\partial x}+\mu\left(\frac{\partial^{2}u}{\partial x^{2}}+\frac{ \partial^{2}u}{\partial y^{2}}+\frac{\partial^{2}u}{\partial z^{2}}\right)+ \rho g_{x} \tag{3}\]  
\[\frac{\partial(\rho v)}{\partial t}+\frac{\partial(\rho v)}{\partial x}+\frac {\partial(\rho v)}{\partial y}+\frac{\partial(\rho wv)}{\partial z}=-\frac{ \partial p}{\partial y}+\mu\left(\frac{\partial^{2}v}{\partial x^{2}}+\frac{ \partial^{2}v}{\partial y^{2}}+\frac{\partial^{2}v}{\partial z^{2}}\right)+ \rho g_{y}\]  
\[\frac{\partial(\rho w)}{\partial t}+\frac{\partial(\rho uw)}{\partial x}+\frac {\partial(\rho vw)}{\partial y}+\frac{\partial(\rho ww)}{\partial z}=-\frac{ \partial p}{\partial z}+\mu\left(\frac{\partial^{2}w}{\partial x^{2}}+\frac{ \partial^{2}w}{\partial y^{2}}+\frac{\partial^{2}w}{\partial z^{2}}\right)+ \rho g_{z}\]  
where \(\rho\) is density [kg/m\({}^{3}\)], \(u\), \(v\), and \(w\) are velocity components in the \(x\), \(y\), and \(z\) directions [m/s], \(p\) is pressure [Pa], \(\mu\) is dynamic viscosity [Pa\(\cdot\)s], and \(g_{x}\), \(g_{y}\), and \(g_{z}\) are acceleration due to gravity in the \(x\), \(y\), and \(z\) directions [m/s\({}^{2}\)]. The continuity equation asserts that the alteration in mass within a control volume must be offset by the mass movement across its boundaries. In simpler terms, the total mass fluxes along the \(x\), \(y\), and \(z\) axes should sum up to zero, ensuring mass continuity. Conversely, the momentum equations illustrate how momentum changes in each direction due to certain factors, like convection, pressure gradients, viscosity, and gravity.