## 2 Materials and Methods
### Numerical Methods  
The structure of the simulations was divided into three parts. The first simulation model set was built based on 1D simulation data. These simulations were used to determine the gas exchange process and exact oxygen content in the cylinder without spray and combustion to precisely determine the injected mass per cycle, because experimental data was unavailable. The results of the first set of simulations will not be presented in this paper. The second set of models contains all the physical models which are necessary to simulate a real engine cycle. These simulations are calibrated against the experimental data with E10 fuel. The last phase of the simulations run on E20 fuel. They are made from the previous set of simulations, assuming the predictability as no E20 experimental data was available. These simulations have the same circumstances, except the fuel. Naturally, with the increase in ethanol content, the higher laminar flame speed allows for a reduction in spark advance. However, this study does not address modifications to spark timing. Additionally, due to the higher oxygen content, the mixture would become leaner if the \begin{table}
\begin{tabular}{c c} \hline
**Data** & **Value** \\ \hline Stroke [mm] & 92.8 \\ Connecting rod length [mm] & 144 \\ Compression ratio [-] & 12.2:1 \\ Displacement [cm\({}^{3}\)] & 1984 \\ Injection type & Direct injection \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **OP1** & **OP2** & **OP3** & **OP4** \\ \hline RPM [1/min] & 2000 & 2500 & 3000 & 3500 \\ BMEP [bar] & 4 & 16 & 20 & 20 \\ Ignition timing [CAD] & \(-\)19.14 & \(-\)2.646 & 0.251 & 1.226 \\ Lambda [-] & 0.999 & 0.999 & 0.997 & 0.949 \\ \hline \end{tabular}
\end{table} 
Table 2: Operating points parameters. amount of injected fuel were not corrected. In this study, the injected fuel quantity was adjusted to ensure that the air-fuel ratio matches that of the E10 cases. The CONVERGE CFD (Version 3.1) software package was used for pre-processing and running the simulations. This software is employed to calculate three-dimensional turbulent reacting fluid flows in complex geometries including moving elements. Using the cut-cell Cartesian method, this code automatically generates the mesh during runtime. This allows the use of a simple orthogonal mesh which represents the boundary shape precisely. The meshing system contains user-defined functions to change the mesh resolution locally during the simulation. Also, it features Adaptive Mesh Refinement (AMR), which refines the mesh based on the gradient of the variables, such as temperature or velocity [26]. The SAGE detailed chemistry solver was used to model combustion phenomena. This chemistry solver solves detailed chemical kinetics via a reaction mechanism file, which contains chemical kinetics properties of species. A built-in feature called multi-zone was used to accelerate the solving process [27]. A reaction mechanism which was mostly based on [28] with 201 species and 1013 reactions was used for the following simulations. Two fundamental requirements for combustion are mixing and chemical reactions. In numerical simulations, the mixing process is primarily governed by the turbulence model. Several studies have demonstrated that the RNG \(k\)-\(\epsilon\) turbulence model is well-suited for simulating combustion in internal combustion engines [29; 30; 31]. In recent years, large eddy simulation (LES) models have gained increasing popularity due to their ability to resolve more detailed flow structures. However, Reynolds-averaged Navier-Stokes (RANS) models, such as the RNG \(k\)-\(\epsilon\), remain widely used due to their significantly lower computational cost [32]. Pressure-velocity coupling was handled using the PISO algorithm, and a pressure-based solver was employed for the simulations. Spatial discretization of the governing equations was performed using a first-order non-conserving upwind numerical scheme to ensure repeatability.