## 1 Introduction
[PERSON] [26] explored the impact of spatial dimensions on flow control areas for jet propulsion device performance and proposed suitable fluid domain control volume sizes for predicting jet propulsion device performance. Additional research utilizing numerical methods focuses on topics like the effect of sediment-laden flows on propulsion efficiency [27]. Recently, there have been many more interesting studies related to hydrodynamics and control strategies of underwater mechanical systems, such as the control and monitoring of underwater robots. The conclusions and research methods of these studies provide valuable insights for research on submaribles [28; 29; 30]. For example, [PERSON] [31] applied a combined approach to predict the lateral hydrodynamic coefficients of underwater gliders, indicating that boundary layer theory is effective in studying the frictional resistance and splash drag of underwater gliders. [PERSON] [32] investigated the unsteady motion of gliders in waves and boundary element methods to determine the hydrodynamic coefficients such as lift, drag, and pitch due to wave-induced motions, comparing their results with [PERSON]'s experimental findings and noting a high level of agreement. [PERSON] [33] created models of various types of underwater gliders through 3D modeling and predicted the hydrodynamic characteristics of different glider types using a boundary element-based method. [PERSON] [34] and [PERSON] [35] studied podded propulsors using a velocity-based unsteady panel method and equivalent two-dimensionalsections to forecast the effects of yaw angle on propulsion thrust and moments, as well as cavitation and other unsteady hydrodynamic phenomena, exploring the cavitation characteristics of propeller blades and pods. [PERSON] [36] and collaborators conducted simulation validation of the hydrodynamic maneuvering performance of submarines using 50 processors, simulating overtaking experiments in the vertical and horizontal planes, and analyzing the flow fields under different steering conditions. [PERSON] [37] simulated turning maneuvers of large vessels and observed an increase in torque with increasing drift angle during turning, noting variations in handling performance with changes in drift angle and sailing speed. [PERSON] [38] employed a multi-blade structure for the propeller to ensure sufficient structural strength during submarine navigation, using fuzzy logic control to simulate submarine motions and examining the guiding effect of turbulent vortices on submarines' vector thrust in turbulent environments. [PERSON] [39] combined numerical simulations with wind tunnel tests to study the distribution of surface pressure and shear stress during inclined motion of submarines, investigating the vortex core positions on the backflow face of the submarine. Although significant research progress and important conclusions have been achieved through numerical research methods, a clear understanding of the dynamic behaviors of submarines during yaw and heading motions is still lacking and requires further in-depth and systematic study. This article first introduces the geometric parameters and performance parameters of the research object and presents the basic research theory of submarisbles. Then, using numerical methods and dynamic mesh technology combined with a circulating water tank experiment, the horizontal yaw dynamic characteristics of pump-jet-propelled submernsides are studied. This study focuses on the effects of pitch angle, screw centrifugal pump speed, and vector nozzle angle on lateral force and lateral moment during oblique sailing and yaw motion processes. The evaluation of the submersible's velocity coefficient and angular velocity coefficient is based on the least squares method. Numerical simulation results are verified for reliability through submersible mooring and simulated cruising experiments. This study provides a theoretical foundation for establishing a mathematical model of the horizontal maneuverability of submersibles.