High-Frequency Pressure Fluctuation (HFPF) is an extensively observed hydraulic phenomenon in pumped-storage power stations and water conveyance projects. The investigation of the propagation characteristics of the pressure perturbation is of great significance for the safe operation of hydraulic facilities. In this study, a one-dimensional (1D)–three-dimensional (3D) coupling model is established based on the combination of the Method of Characteristics (MOC) and Computational Fluid Dynamics (CFD) and implanted in the open source software OpenFOAM. The established model in this study implants the dynamic mesh module into the original OpenFOAM solver sonicLiquidFoam and presents the complete solution procedure of the CFD model with the dynamic mesh considered. The vibration of the pipe walls modeled by the mesh motion is employed to numerically generate the HFPF in the hydraulic system, which could not be implemented in the traditional MOC model. The independence of the pressure perturbation in the pipeline system is validated by the time-domain pressure variation. The graphical method is applied to describe the multiple reflection and superposition characteristics of the traveling wave in a simplified hydraulic system. Based on this, the mechanism of the superimposed characteristic of the traveling and standing pressure waves in the hydraulic system are analyzed, and the theoretical superimposed time-domain processes and the variations of the pressure oscillation magnitude are analyzed and presented. The 1D–3D coupling method and the theoretical analysis method could be referenced by other complex hydraulic systems.