## 3 Numerical Modeling and Code Validation  
For simulation of the infusion process, the conservation equations of mass, momentum, and transport equation of volume fraction were solved using a commercial CFD (computational fluid dynamics) code based on FVM [39; 40; 41]. Numerical simulations were carried out using computers with 4 Intel Xeon processors and 8 threads of 3.30 GHz clock and 8.0 Gb of RAM. In all the simulations, the second-order upwind discretization scheme was used for the treatment of the advective terms. For pressure interpolation, the PRESTO scheme was used. Pressure-velocity coupling was performed with the PISO method, while the Geo-Reconstruction method was used to reconstruct the interface between the two fluids. In addition, sub-relaxation factors of 0.3 and 0.7 are imposed for the conservation equations of mass and momentum, respectively. The simulations are considered converged when the residuals of conservation equations of mass and momentum are lower than \(R<10^{-6}\). For time discretization, a study of time step independence was performed, since a transient problem was being investigated. Five simulations were performed with a varying time step, and its influence over the volume of domain completely impregnated by the resin was investigated, i.e., the volume of domain with volume fraction of \(f=1.0\). For all simulations, the volume of resin injected up to time of \(t=7.0\) s was evaluated. Table 1 shows, for the analyzed injection time, the volume percentage of the domain filled with resin and the processing time required to carry out the simulations. The analyzed case consists of a I-shaped empty channel with area fraction of \(\phi=0.05\), \(H\)/\(L=1.0\) and \(L_{0}\)/\(H_{0}=4.0\). It is possible to observe that for values of \(\Delta t\leq 1.0\times 10^{-3}\) s, all employed time steps lead to identical results. For the values of \(\Delta t=1.0\times 10^{-2}\) s and \(\Delta t=1.0\times 10^{-1}\) s, there is no convergence in the simulations. Consequently, the time step of \(\Delta t=1.0\times 10^{-3}\) s is adopted in subsequent geometric evaluation simulations, as it leads to a lower computational effort compared to smaller time steps. For spatial discretization, the domain was divided into finite rectangular volumes, and a mesh independence test was performed to define the number of volumes used for the simulations. The time step used is defined in Table 1 (\(\Delta t=1.0\times 10^{-3}\) s). Table 2 shows the number of volumes, the filling time for complete impregnation of resin in the mold, and the processing time required to perform the simulations for each evaluated mesh and for the same I-shaped channel studied in the time independence study, i.e., \(\phi=0.05\), \(H\)/\(L=1.0\) and \(L_{0}\)/\(H_{0}=4.0\). The following equation presents the criterion for achievement of an independent mesh:  
\[Difference=\frac{100\cdot\left|t^{j}-t^{j+1}\right|}{t^{j}}<1.0\% \tag{12}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time Step (s)** & **Mold Filling (\%)** & **Processing Time (s)** \\ \hline \(1.0\times 10^{-5}\) & 27.1596 & 171,000 \\ \(1.0\times 10^{-4}\) & 27.1596 & 8900 \\ \(1.0\times 10^{-3}\) & 27.1596 & 1200 \\ \(1.0\times 10^{-2}\) * & — & — \\ \(1.0\times 10^{-1}\) * & — & — \\ \hline \hline \end{tabular}  
* Non-converging solutions.  
\end{table} 
Table 1: Study of sensibility of time step over resin impregnation for an I-shaped empty channel with \(\phi=0.05\), \(H\)/\(L=1\), and \(L_{0}\)/\(H_{0}=4\). where \(t^{j}\) represents the minimum value of the filling time calculated with the coarser mesh, and \(t^{j+1}\) corresponds to the magnitude calculated with the refined successive mesh. Successive refinements determine appropriate mesh size until the magnitude of the difference variable for two successive meshes is lower than 1.0%. In this sense, a mesh with 18,271 finite rectangular volumes is used in this study.