## 2 Methodology and Model Descriptions
### Model Specifications  
In this study, a commercial CFD software, CONVERGE, was adopted to carry out numerical simulation for the closed part of the engine cycle, namely from IVC (intake valve close) to EVO (exhaust valve open), and the main specifications of the gasoline engine (produced by Chery Automobile Co., Ltd., in China) are shown in Table 1. The computational mesh of the engine geometry is illustrated in Figure 1, and the high-quality orthogonal hexahedral meshes were obtained through CONVERGE codes. In order to keep a tradeoff between computation resolution and efficiency, the AMR strategy was adopted to automatically modify meshes, subject to the distribution of local velocity, temperature and the corresponding species mass fraction [11]. In this study, a basic mesh size of 1 mm was employed. In addition, one level of invariable boundary embedding was set close to the cylinder head, piston and wall (cell size of 0.6 mm), while three levels of invariable spherical embedding (radius of 0.6 mm) were carried out to solve the spark (cell size of 0.125 mm) [27]. A lot of parametric conditions were taken into account for initial temperatures and pressures shown in Table 2. The non-uniformity temperature distributions in cylinder were taken into consideration such as cylinder head and piston at 550 K and 837 K, respectively. The inhomogeneous temperature was characterized by two kinds of initial conditions. Firstly, to describe global temperature variables, a sinusoidal temperature curve was overlayed on the initial average temperature with a specified root-mean-square variation and wavelength spanning the domain length as illustrated in literature [28]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Bone/stroke (mm) & 74.5/80 \\ Number of cylinders & 4 \\ Compression ratio & 10:1 \\ Fuel supply method & Direct injection \\ Torque (N.m) & 200 (1400 r/min) \\ Rated speed (r/min)/rated power (kW) & 5000/90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main specifications of the engine. Figure 1: Geometry of the engine. In addition, to characterize a local ignition source, a hot spot was represented using a superimposed Gaussian temperature curve [28]. A fuel-air equivalence ratio of 1.05 was set and the mixture was diluted with a certain amount of nitrogen, which ensured not only to serve as an indicator of auto-ignition but also to restrain shock wave coming into being similarly reported in literature [28; 29]. In this study, the working process of the engine was divided into three parts to establish the numerical model, namely the flow process, the spray process and the combustion process. The flow model was used as a preliminary preparation of the combustion model so that the simulations were performed for the intake and compression processes. The simulation calculation period was set in the range from \(-366\)\({}^{\circ}\)CA to \(-20\)\({}^{\circ}\)CA and the turbulent model was the RNG k-\(\varepsilon\) turbulent flow model. Since only the flow of air existed during the simulation of the engine gas flow, oxygen and nitrogen were the main components, so only O\({}_{2}\) and N\({}_{2}\) components needed to be added to the reaction mechanism. The spray process mainly simulated the formation process of fuel spray and air-fuel mixture. It was necessary to add three components of O\({}_{2}\), N\({}_{2}\) and IC\({}_{8}\)H\({}_{18}\), as well as their thermal physical properties and reaction mechanism. The fuel injection starting point of the six-nozzle injector was \(-240\)\({}^{\circ}\)CA and the injection duration was 75 \({}^{\circ}\)CA. The relevant spray sub-models were shown in Table 3.  
The combustion model was established based on the flow model and the spray model. Before the combustion model was established, the flow model and the spray model were calculated to obtain the corresponding results, and the results were then introduced into the combustion model.