## 4 Conclusions and Discussion  
The computation of compressor characteristic curves is a fundamental prerequisite for their design, optimization, and application. Numerical simulation is an exceptionally efficient method to address this problem and is widely adopted by scholars in studying compressors. The crux of characteristic line simulation hinges on ascertaining the precise boundary conditions near the stall point. With the aid of the Isight optimization platform and Numeca CFD solver, this paper automated the compressor characteristic simulation process and applied these methods to a specific single-stage compressor. Initially, the automatic resolution process of characteristic curves governed by the dichotomy method parameter stipulations was implemented, where pivotal aspects encompass convergence determination and parameter settings. Through two loops, the stall margin interval was established, and thereafter, the specific boundary condition of the stall point that conforms to the desired solution accuracy was specified. Then, the optimization algorithm workflow for pinpointing the stall point was proposed and improved. Upon evaluation, both methods were able to automatically solve the compressor characteristic curves. In terms of computational load, the dichotomy method required fewer computation resources for the subject tested in this study. The optimization algorithm workflow still needed to iterate a certain number of cycles after determining the interval to satisfy the criteria of the optimal solution. In general, the differences between the two methods are primarily determined by the pressure spacing interval and the required precision. Further refinements were applied to the process utilizing the optimization algorithm by eliminating the loop that ascertains the stall margin interval and directly converting the problem into a given boundary optimization solver. Results demonstrate that the direct optimization solution notably reduced computational demands compared to the dual-loop optimization workflow, offering a significant advantage. These findings suggest that in the simulation of compressor characteristic curves, if the stall interval can be roughly ascertained, the dichotomy method may be more efficient. If the determination of the compressor's stall interval is imprecise, a direct optimization solution becomes more efficacious. The method introduced herein facilitates the characteristic curve automation process, which is beneficial for enhancing the efficiency of the performance simulation process while ensuring result consistency and mitigating errors potentially arising from manual intervention. Though the methodology has been validated through the solution of single-stage compressor characteristic curves, it may also extend to the solution of other turbomachinery characteristic curves and linear cascade characteristics. When it is necessary to calculate multiple characteristic curves at varied rotational speeds or incidence angles, an added Design of Experiments (DOE) phase to the presented method suffices. Furthermore, the  
Figure 9: Iteration history of the outlet boundary condition using direct optimization workflow. current research's accomplishment paves the way for the subsequent comparative analyses of different optimization algorithms' efficiency. J.L. : Methodology (lead); Writing--original draft (lead); Writing--review and editing (lead); Software (lead); Visualization (lead). X.F. : Funding acquisition (lead); Conceptualization (lead); Supervision (lead); Writing--review and editing (supporting). X.T. : Methodology (supporting); Writing--original draft (supporting). All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China (grant number: 11872071 and 12102470) and NUDT Research Project (grant number: ZK20-05). Not applicable. The data that support the findings of this study are available from the corresponding authors upon reasonable request.