## 3 Numerical Modeling and Code Validation
To show the reliability of the present computational model, a verification of the numerical method used here was done by comparing the present numerical solution and a classical analytical solution for the rectilinear case. More precisely, resin advancement as a function of infusion time obtained with the present method and the analytical solution described in [PERSON] et al. [50] and [PERSON] [45] are compared. This comparison can be made for empty channels that lead to rectilinear behavior of resin in the porous medium. For the sake of comparison, a simulation in an I-shaped empty channel with \(\phi\) = 0.05, \(H/L\) = 1.0, and \(L_{0}/H_{0}\) = 19.0, where \(L_{0}\) is equal to \(L\), is chosen. The case with these configurations represents a rectilinear case. An analytical solution for front-line resin advancement as a function of time is given by [50]:  
\[X_{f}=\sqrt{\frac{2 KP_{in}t}{\mu\varepsilon}} \tag{13}\]  
where \(X_{f}\) is the position of the resin front-line (m), \(t\) is the time (s), \(\mu\) is the resin viscosity (Pa/s), \(\varepsilon\) is the porosity, \(K\) is the permeability (m\({}^{2}\)), and \(P_{in}\) is the injection pressure (Pa). It should be noted that the present formulation is only applicable to a constant \(P_{0}\) situation. A monitoring line was created in the center of the domain to obtain the numerical results. More precisely, a line that overlaps the \(y\)-axis was defined by the following points: P\({}_{1}\) (\(x_{1}\) = 0.0 m, \(y_{1}\) = 0.0256 m) and P\({}_{2}\) (\(x_{2}\) = 0.0 m, \(y_{2}\) = 0.7500 m). The coordinates \(x_{1}\) = \(x_{2}\) represent the center of the domain in the \(x\)-direction, while the coordinate \(y_{1}\) represents the interface placement between the open channel and the porous medium, and \(y_{2}\) is the exit region of the resin. Figure 4 shows the advancement of the resin front line as a function of the injection time for both solutions (analytical and numerical) and an illustration of the simulated domain with monitoring points for resin advancement in the porous medium. A maximum difference of 0.66% was observed between the analytical and numerical results, which is an indication of very good agreement. Therefore, the verification of the numerical model presented was satisfactorily achieved, and the code can be used for theoretical recommendations on the geometric configurations of I and T-shaped empty channels inserted in a rectangular porous plate. It is also worth mentioning that the present computational model was previously verified and validated in the work by the authors of [9]. The resin propagation obtained with this computational model was verified with the analytical data for linear and radial cases and with numerical results obtained with the PAM-RTM(r) software for three-dimensional resin flow in a rectangular box and spherical shell. Moreover, the code was validated with the experimental results obtained by [PERSON] et al. [51] for a case of resin flow in a cavity mold with an inlet nozzle. More precisely, it was compared to the results of resin flow advancement as a function of time: differences of nearly 8.0% were found. The cases in Reference [9] mimic resin transfer molding (RTM) or light-resin transfer molding (LRTM) processes. In spite of the simulation of different processes, the fluid dynamic behavior of the resin flow of Reference [9] is the same as performed here. These results were reproduced for \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Volumes** & **Filling Time (s)** & **Difference (\%)** & **Processing Time (s)** \\ \hline
1209 & 188.3 & 1.69 & 43,000 \\
4636 & 185.1 & 1.18 & 78,400 \\
18,271 & 182.9 & 0.87 & 126,500 \\
72,451 & 181.3 & — & 184,900 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mesh independence test considering an I-shaped empty channel with \(\phi\) = 0.05, \(H/L\) = 1.0 and \(L_{0}/H_{0}\) = 4.0.  
code validation in this study, but are not provided here since they have already been presented in Reference [9].