## 1 Introduction  
In the 1970s, the aviation industry introduced simulators for crew training to reduce accidents caused by human error, significantly improving the skill level and decision-making ability of crew members [1]. The success of aviation simulators attracted the attention and emulation of other transportation fields. Since the 1990s, simulators have been widely applied in the maritime industry for training purposes [2]. Among these, the importance of marine engine simulators is particularly prominent [3]. These simulators can vividly reproduce the operation of ship engines and related equipment, providing trainees with a safe and controlled environment where they can practice under various simulated scenarios, experiencing the real feel of a ship [4], including mimicking the engine room and audiovisual effects [5, 6]. This not only allows trainees to master complex engine system operations but also enhances their ability to respond to emergencies. Additionally, marine engine simulators can simulate various potential malfunctions and abnormal situations, enabling trainees to remain calm when facing real failures, thereby effectively reducing mechanical failures and losses due to operational errors [7]. Through marine engine simulator training, trainees can fully understand the operating principles and processes of engine systems without boarding a real ship [8]. This training method not only saves time and costs but also avoids potential dangers during actual operations. Furthermore, marine engine simulators allow for repeated training, enabling trainees to accumulate experience quickly and improve their skills in a short time [9]. An essential component of the marine engine simulator is the ship's piping system. The piping system serves as the \"nervous system\" connecting various critical components of the ship, including the fuel pipelines, cooling water pipelines, and compressed air pipelines [10]. Their reliable operation is fundamental to ensuring the normal navigation and mission execution of the ship [11; 12]. For pipelines, especially flexible ones, connections are often the weakest link. Therefore, advanced software is used to model the hydrodynamic phenomena associated with high-pressure fluid flow in the pipelines. Numerical methods are effective for pipeline design, taking into account hydrodynamic phenomena and potential pipeline failures [13]. The simulator realistically reproduces the design and operational conditions of these piping systems, enabling trainees to fully master their operational techniques and thereby reduce human error. It should be noted that modeling the flow inside the pipeline is crucial even at the design stage, as it helps predict the maximum load on the pipeline and design its length, wall thickness, and the number and position of supports. When the working fluid is flowing, especially in long pipelines, the water hammer effect can cause damage or even rupture the pipeline. Therefore, using advanced software to model the hydrodynamic phenomena associated with high-pressure flow is essential. The simulator's realistic reproduction of the design and operation of these systems enables trainees to master operational techniques fully, reducing human errors [14]. However, programming the ship's piping system is highly complex and typically requires programmers to handle large amounts of data, which is inefficient. As a result, there has been growing interest in visual modeling methods for ship piping systems within marine engine simulators, with a focus on dynamic modeling, neural networks, modular modeling, and real-time simulation capabilities. These studies highlight the importance of accurate mathematical models and visual simulation in improving training and operational efficiency in the maritime industry. In response, this paper proposes a visual modeling method for the ship's piping system. Through this method, the complex programming of the engine piping system becomes more intuitive and efficient, greatly enhancing data processing efficiency.