The Reynolds equation, in which some items have been omitted, is a simplified form of the Navier-Stokes equations. When surface texturing exists, it may unreasonably reveal the tribological effects in some cases. In this paper, both the two-dimensional computational fluid dynamics method, which is based on the Navier-Stokes equations, and the corresponding one-dimensional Reynolds method are adopted to analyze the performance of the textured piston compression ring conjunction. To conduct a comparison between these two methods, the modified Elrod algorithm for Jakobsson-Floberg-Olsson cavitation model is chosen to solve the Reynolds equation. The results show that the Reynolds method is somewhat different from the computational fluid dynamics method in the minimum oil film thickness, pressure distribution, and cavitation at given operating conditions. Moreover, for a low ratio of texture depth to length, the Reynolds equation is still suitable to predict the overall effects of the designed groove textures. The simulation results also reveal that it is not always beneficial for the tribological performance and sometimes may increase the total friction force when the ring is textured.